コンプリート！ differentiate the function. y = x (x − 8) 291710-Differentiate the function. y = 8x2 + 8x + 8 x

 The binomial theorem tells us that (a b)3 = a3 3a2b 3ab2 b3 Putting a = x,b = x−1 gives (x x−1)3 = x3 3x2x−1 3x(x−1)2 (x−1)3 = x3 3x 3x−1 x−3 This can be easily differentiated using the rule that d dx xn = nxn−1 to get  The answer is x − 4 √x2 −8x y = √x(x −8) ⇒ y = √x2 − 8x ⇒ y' = 1 2√x2 − 8x ⋅ (2x −8) = 2(x − 4) 2√x2 −8x = x −4 √x2 − 8x The second derivative of function is f " (x) = x * sin(x) 2 Points of Inflection If (c, f(c)) is a point of inflection of the graph of f(x), then either f " (c) = 0 or f " (x) does not exist at x = c Graph for f " (x) = x * sin(x) 2 Observe the graph, the graph crosses the xaxis at four places, so the number of points of inflection of the graph of f(x) is four in the interval (10, 10)

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Differentiate the function. y = 8x2 + 8x + 8 x

Differentiate the function. y = 8x2 + 8x + 8 x-Stepbystep solution 92% (25 ratings) for this solution Step 1 of 5 Consider the following function Differentiate the given function, with respect to x Let, then the function will be as follows Use the chain rule, to differentiate the function with respect to x Since,Y2 x3 −y3 6 = 3y with respect x We differentiate each term with respect to x d dx y2 d dx x3 − d dx y3 d dx (6) = d dx (3y) Differentiating functions of x with respect to x is straightforward But when differentiating a function of y with respect to x we must remember the rule given in the previous keypoint We find d dy y2 ×

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Derivative of a Constant lf c is any real number and if f(x) = c for all x, then f ' (x) = 0 for all x That is, the derivative of a constant function is the zero function It is easy to see this geometrically Referring to Figure 1, we see that the graph of the constant function f(x) = c is a horizontal lineThere are two ways we can find the derivative of x^x It's important to notice that this function is neither a power function of the form x^k nor an exponential function of the form b^x, so we can't use the differentiation formulas for either of these cases directly (i) Let y=x^x, and take logarithms of both sides of this equation ln(y)=ln(x^x)Textbook solution for Single Variable Calculus 8th Edition James Stewart Chapter 6 Problem 27RE We have stepbystep solutions for your textbooks written by Bartleby experts!

Textbook solution for Single Variable Calculus Concepts and Contexts, 4th Edition James Stewart Chapter 36 Problem 28E We have stepbystep solutions forFunction Derivative y = a·xn dy dx = a·n·xn−1 Power Rule y = a·un dy dx = a·n·un−1 du dx PowerChain Rule Ex1a Find the derivative of y = 8(6x21)8 Answer y0 = 384(6x 21)7 a = 8, n = 8 u = 6x21 ⇒ du dx = 6 ⇒ y0 = 8·8·(6x21)7 ·6 Ex1b Find the derivative of y = 8 4x2 7x28 4 Answer y0 = 32(8x 7) 4x2 7x 28 3 a You can use logarithmic differentiation Take the natural logarithm of both sides lny = lnxx Now using properties of logarithms, rewrite the right hand side lny = xlnx Differentiate both sides with respect to x Use the product rule on the right side 1 y

Solution for Differentiate y = 2x 7 − tan(x Q Sketch the graph of a function by a) finding all vertical and horizontal asymptotes of the function, A Note In given problems, there are subparts and many questions, I will answer the 1st question and tThe slope of a line like 2x is 2, or 3x is 3 etc; For example if y = f(x,y), is a function depending on two variables 'x' and 'y', then the partial derivative of 'f' with respect to 'x' is obtained by assuming the variable 'y' to be a constant and taking the derivative of 'f' with respect to 'x' This is represented as f (x, y) ∂x ∂ Example 8 If y = xsin(t

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Explanation Step 1 1 of 8 We can rewrite the fraction It's more simple for viewing the next step y = ( x − 1) 1 2 ( x 4 1) 1 2 y= \dfrac { (x1)^ {\frac {1} {2}}} { (x^41)^ {\frac {1} {2}}} y = ( x 4 1) 2 1 ( x − 1) 2 1 Step 2 2 of 8 We use two logarithms rules (power rule and quotient rule) toThe fourth derivative of the function f (x) = x 5 − 3 x 4 2 x 3 − x 2 4 x − 10 is A 1 B 1 x C 1 x − 72 D 60 x 2 − 72 x 12 12 The equation of the tangent line to y = x 2 − 4 x 2 at (4, 2) is equal to A y =− 4 x 14 B y = 4 x − 14 C 4 x y 14 = 0 D − 4 x − y − 14 = 0Differentiate the following function y = x^8 e^x dy/dx = Find f′(x) f(x) = 6x e^x f′(x) = Find f′(x) f(x) = 2x x − 8 4 3 f′(x) = Find the indicated derivative and simplify y′ for y = 5 6x − 4x e 2 x y′ = Question Differentiate the following function y = x^8

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1) Differentiate the following function y=x−7/8 2Differentiate y=ex /7x2 Option 1 Low Cost Option Download this past answer in few clicks 286 USD PURCHASE SOLUTIONDifferentiate the function y = e^(x1) 1Implicit differentiation is nothing more than a special case of the wellknown chain rule for derivatives The majority of differentiation problems in firstyear calculus involve functions y written EXPLICITLY as functions of x For example, if However, some functions y are written IMPLICITLY as functions of x

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To perform implicit differentiation on an equation that defines a function implicitly in terms of a variable use the following steps Take the derivative of both sides of the equation Keep in mind that y is a function of x Consequently, whereas because we must use the chain rule to differentiate with respect toLet y=x 2cosxDifferentiate it with respect to x using by parts dxd(uv) =u dxdv v dxdu so, dxdy =x 2(−sinx)cosx(2x)dxdy =2xcosx−x 2sinxAnswer to Differentiate the following functions f ( x ) = x 4 y = t − 3

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Calculus Find the Derivative d/dx y=8^x y = 8x y = 8 x Differentiate using the Exponential Rule which states that d dx ax d d x a x is axln(a) a x ln ( a) where a a = 8 8 8xln(8) 8 x ln ( 8)Find the Derivative d/dx y=x^(8cos(x)) Use the properties of logarithms to simplify the differentiation Tap for more steps Rewrite as Expand by moving outside the logarithm Differentiate using the chain rule, which states that is where and Tap for more stepsClick here👆to get an answer to your question ️ Differentiate the given function wrt x x^x^2 3 (x 3)^x^2 , for x > 3

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The Derivative tells us the slope of a function at any point There are rules we can follow to find many derivatives For example The slope of a constant value (like 3) is always 0;I read it as the square root of that quantity You would use the quotient rule to solve this (F'gg'f)/g 2 You would use the chain rule D/dx =q/2 (8x 2 6x2) 1/2 (16x6) This particular chapter I'm on talks about using the product ruleSolution for a) Differentiate the function y = etan(θ) Differentiate the function b) f(z) = ez/(z − 8) Differentiate the function c) F(t) = e2t

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Cases in which n is a positive integer as in the functions x2, x7 and so on 2 Differentiation of y = xn when n is a positive integer Recall the definition of the derivative of a function y = f(x) dy dx = lim δx→0 f(x δx)− f(x) δx We apply this definition to the function y = xn We have f(x) = xn and so f(xδx) = (x δx)nY ' (1 / y) = ln x x (1 / x) = ln x 1 , where y ' = dy/dx Multiply both sides by y y ' = (ln x 1)y Substitute y by x x to obtain y ' = (ln x 1)x x Exercise Find the first derivative of y = xx 2 Answer to Above Exercise y ' = x x 3 (x ln x x 2) More on differentiation and derivativesThe derivative of a function y = f(x) is the function defined by f0(x) = lim h→0 f(xh)−f(x) h So the derivative f0(x) of a function y = f(x) spews out the slope of the tangent to the graph y = f(x) at each x in the domain of f where there is a tangent line One thing we will have to deal with is that there is quite a variety of

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In this case we can find out what that function is explicitly simply by solving for y Sometimes, however, we must deal with equations relating y to x that are so complicated that it is difficult or even impossible to solve for y in terms of x (For example, try to solve for yin the equation y y xy = 10) If an equation implicitly defines y as a function of x, there is a way to find dy/dx without firstDifferentiate wrtx the function in Exercise 1 to 11 x x 2 − 3 ( x − 3) x 2 for , x > 3 Medium View solution > Differentiate the following function x 3 x 2 4 x − 5 MediumCalculus Examples Popular Problems Calculus Find the Derivative f (x)=x^8e^x f (x) = x8ex f ( x) = x 8 e x Differentiate using the Product Rule which states that d dxf (x)g(x) d d x f ( x) g ( x) is f (x) d dxg(x)g(x) d dx f (x) f ( x) d d x g ( x) g ( x) d d x f ( x) where f (x) = x8 f ( x) = x 8 and g(x) = ex g ( x) = e

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Start with y = sin−1 (x) In non−inverse mode x = sin (y) Derivative d dx (x) = d dx sin (y) 1 = cos (y) dy dx Put dy dx on left dy dx = 1 cos (y) We can also go one step further using the Pythagorean identity sin 2 y cos 2 y = 1 cos y = √ (1 − sin 2 y ) And, because sin (y) = x (from above!), we getCalculator solves the derivative of a function f(x, y(x)) or the derivative of an implicit function, along with a display of the applied rules Enter expression and press or the button Options Settings Functions Differentiate by autocorrect = ¹²− ⌫ = sin cos tan cot 𝜋Differentiate the function y = x^(2/5)

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And so on Here are useful rules to help you work out the derivatives of many functions (with examples below)Note the little mark ' means derivative of, andY = xe^(x^2), Find the derivative of the function ProblemSolving Strategy Implicit Differentiation To perform implicit differentiation on an equation that defines a function implicitly in terms of a variable , use the following steps Take the derivative of both sides of the equation Keep in mind that is a function of Consequently, whereas and because we must use the chain rule to

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Differentiate the given function wrt x y = sin (tan − 1 e − x) Medium View solution > Differentiate the given function wrt x y = lo g (cos e x) Medium View solution > Differentiate the given function wrt x e x 3 Easy View solution > Differentiate the given function wrt x 3 Eliminate the exponent Using the rules of logarithms, this equation can be simplified to eliminate the exponent The exponent within the logarithm function can be removed as a multiple in front of the logarithm, as follows ln ⁡ y = x ln ⁡ a {\displaystyle \ln y=x\ln a} 4 Differentiate both sides and simplifyDifferentiate the function y = (x^2 4x 3)/sqrt(x)

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Since 1 8 1 8 is constant with respect to x x, the derivative of x 8 x 8 with respect to x x is 1 8 d d x x 1 8 d d x x Differentiate using the Power Rule which states that d d x x n d d x x n is n x n − 1 n x n 1 where n = 1 n = 1 Multiply 1 8 1 8 by 1 1 Evaluate d dx − 8 x d d x 8 xSince − 9 9 is constant with respect to x x, the derivative of − 9 x 9 x with respect to x x is − 9 d d x x 9 d d x x Move − 9 9 to the left of x 2 x 2 Differentiate using the Power Rule which states that d d x x n d d x x n is n x n − 1 n x n 1 where n = 1 n = 1 Multiply − 9 9 by 1 1A given point 0,2,2 given plane xyz=3 given line x=1t,y=2t,z=2t question_answer Q Write the equation of the tangent line to the curve at the indicated point

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Incoming Term: differentiate the function. y = x 8 + x, differentiate the function. y = 2x2 + 8x + 8 x, differentiate the function. y = 6x2 + 8x + 8 x, differentiate the function. y = 4x2 + 8x + 8 x, differentiate the function. y = 8x2 + 8x + 8 x,