Find f'(a) for 6. f(x) = %3D V6-47 18 f'(a) = (-4x+ 0)*

Q: Find dy/dx by implicit differentiation   2x3 +x2y  -xy3  = 2

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Q: finf dy/dx by implicit differentiation when x^2=(3x+6y)/(3x-6y).

A: The given function is: x2=3x+6y3x-6y

Q: How to solve for the derivative of Dy[tan(y)+1/tan(y)-1]? If it's 0, why?

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Q: 14. If x2 + y2 13, find at (2, 3). dx2 %3D

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Q: 3.

A: Indefinite Integration

Q: Find  dy dx by implicit differentiation. tan−1(4x2y) = x + 5xy2

A: tan−1(4x2y) = x + 5xy2 We differentiate both sides with respect to x using the product rule and…

Q: Estimate the instantaneous rate of change of y(x) 4 at the %3D x+ 1 point x = - 2

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Q: Find the derivative. 2 - - dy dx - if y(x) = 1 x + 3 dy dx ||

A: This question is based on Chain rule diffrentiation. d/dx{f(x).g(x)} = g(x)d/dx{f(x)} +…

Q: Estimate the second derivative of f (x) = difference approach with h=O.1? 25x3 6x2 + 7x -88 at x-2,…

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Q: If the instantaneous rate of change of ƒ(x) with respect to x is positive when x = 1, is ƒ…

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Q: Find the average rate of change of f(x)=x² – 5x from: x, =-1 to x, = 3

A: We will find the average rate of change of the function.  We know,  the average rate of change =…

Q: Find the instantaneous rate of change of y with respect to x at x=2 of the function y = 2x³ + 4 %3D

A: To Find: The instantaneous rate of change of the function y=2x3+4 at x=4. Given: The function is…

Q: Estimate ln(0.9) using a linear approximation

A: Given:ln(0.9)

Q: 2. Estimate the instantaneous rate of change of y = at x = 1. Show your work. 2x-3x+1

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Q: Determine the percentage relative error (In 2 decimal places) when we compare the derivative of…

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Q: 10. S(2x – 3) dx e 2x2 - ебх

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Q: 4 1 Y(s) = 5s2

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Q: The total derivative of f(x,y) = ylnx  is

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Q: Differentiate: F(y) (y + 9y°) yA - y?

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Q: Estimate the instantaneous rate of change at the point x=2 for f(x)=ln(x) ROC =

A: the fiven function is f(x)=ln(x)

Q: If the instantaneous rate of change of ƒ1x2 with respect to x ispositive when x = 1, is ƒ increasing…

A: As instantaneous rate of change  of f(x) that is f'(x) is positive means the function f(x) is…

Q: Find one anti derivative of (x+1)^2 and then find  integral(x+1)^2 dx.

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Q: Calculate the derivative.

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Q: Find the instantaneous rate of change of g(x) = In(x + 3) at x =

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Q: dx V9-x2

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: rdr 17. S- V16-9r4 dy 18. S; 3x2-2x+5

A: Given

Q: Find anti derivative 3x^2(y^2+1)

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Q: Find dy/dx by implicit differentiation of 6x3+x2y-xy3=4

A: Product rule of differentiation:If f(x) is a function of u and v where both u and v are variables…

Q: Find the rate of change of f (x) = x° at x = 2. %3D

A: Rate of change.

Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 60x + 0.9x? –…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: What is the difference of antidifferentiation and anti-derivative?

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Q: Determine the instantaneous rate of change of the function πt³ √x sin (TE³ 2 f(x) = x3 1 + √t at…

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Q: What is the instantaneous rate of change of the function f ( x ) = 5 /x  at x = 3 ?

A: Given,        The instantaneous rate of change of the function fx=5x at x=3.We know that,…

Q: Find the average rate of change of LaTeX: f\left(x\right)\:=3x^2+1 f ( x ) = 3 x 2 + 1 between…

A: Formula for average rate of change is f(b)-f(a)b-a.

Q: water leaking onto a floor creates a circular pool with an area that increases at the rate of 3…

A: Let  A=π r2 differentiating A with respect to time tdAdt=2πr…

Q: Determine the derivative -d/dv y = 2x³ + 5x - 6 y 1 x² 3x 6x³ + x² − 10x − 3 -

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Q: Find the 2nd derivative of the given function fCt) = t² Int

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Q: Find teh average rate f change of f(x)=3x^(2)-x from x_(1)=-1 to x_(2)=2

A: Solution: The objective is to find the average rate of change of the given function

Q: Find the derivative of the function f(x) = (3+arctanx)^(ln(x^2 +1))

A: Apply exponent rule:

Q: nd derivative of f(x) = x In(x)

A: We have to find the second derivative of the given function

Q: find implicit derivative dy/dx of x2sin2(y)+2x2=y

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Q: compute the rate of Change of the functioN at x= a. flx)= -2X²-X,Q= -5 instantaneous

A: Given function: fx=-2x2-x

Q: . Use a similar procedure to estimate the instantaneous rate of change of y = 3" at r = 0. Show your…

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Q: 4x dx

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Q: Calculate Calculate 1 f (425 - / +6²-8) dz 4x - dx. X S 5² - -x³√x² + 3 dx 3 ln³ Calculate 41³ (2)…

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Q: What is the difference between a derivative and an integration?

A: We have to state the difference between a derivative and integral.

Q: Suppose x and y are functions of third variable t. In the equation *-+) , what are the values of the…

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Q: Find the derivative of s(*) - L Int dt 1+t

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Q: What is the average rate of change of f(x)= x2 -2 on the interval [-1,3]?

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Q: 6. Use the difference quotient to estimate the 2 instantaneous rate of change in f(x) = x² at x=3…

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