For the function f(x) = 3 e -X, find f''(x). Then find f''(0) and f''(1). f"(x) = 48x° e -x* - 36x² e %3D Select the correct choice below and fill in any answer boxes in your choice. O A. f'(0) = (Simplify your answer.) B. f'(0) is undefined.

Q: Find the derivative of the function. 1 In(1 + 49x 14 y = x arctan 7x dy

A: Given y = xtan-1(7x) -114ln(1+49x2)dydx = d xtan-1(7x) -114ln(1+49x2)dxdydx =…

Q: Determine the first derivative of the ff. function dz y = e? sin x + In x (arcsin z) with dx 4

A: Determine the first derivative of the function                   y=ez sin x + ln x (arcsin z)  With…

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Q: Find the differential of the function: y = x In x

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Q: 1. Find dy/dx if cos 4y+ysin x =3 2. Use implicit differentiation to find the slope of the tangent…

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Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: (x2-3x)3 1. у 3 ; d'y/dx

A: Question 1,Given,            y=x2-3x3xTo find : d3ydx3

Q: Find dy/dx by implicit differentiation. 52) x3 + y3 = 5

A: Given implicit function : x3+y3=5

Q: Find the differential dy of the given function y=extanx

A:

Q: 7) Find dx 4e* dy if y = %3D 8) Find the first derivative of f (x) = sin? (x°).

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Q: dy by implicit differentiation if dx 3 9. = 1. Find - -

A: The given function is 3y+9x=1

Q: Find the slope of the curve 2xy = In(e*) sin(x) at the point (2,2)

A: to find the slope differentiate  the equation with respect to x .

Q: Find the differential d8y of the function y=exsinx.

A:

Q: Can you help me step by step?

A: Differentiate with respect to x,

Q: 4. Consider the function f(x) = 2 cos x x2 find its derivative

A: (4) Consider the given function. fx=2cosxx2 The quotient rule is defined as. fxgx'=f'g-g'fg2

Q: A// Find the derivative of y with respect to x 5) 3tan-1x + sin-1x = 4 6) y = ln- 1+ ex = la,

A:

Q: i) Find the derivative of g(x)= 4x2 ii) If y³+2y-4x=5 find dy/dx cosx

A: Given: (i) g(x)=cos(x)4x2(ii) y3+2y-4x=5

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Q: Find the most general antiderivative of f(x) = -3e" + 10 sec2 (x), where - < x < 2 Note: Any…

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A:

Q: 4. FIND d²y BY IMPLICIT DIFFERENTIATION: x² + y² = 81 %3D dx2

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Q: The derivative of: y =0( sin (In (0))) in (In (0))) + cos(ln (0)) is is:

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Q: What is the 4th derivative at x = 0 of the function f(z) = (2r + 1)* %3D

A:

Q: Find dy/dx by implicit differentiation. x2 + xy - y2 = 4

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Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = e(x*+1) 3- xy + x²y = 3 at x = 1 4-…

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Q: the derivative of y with respect to v. 1 = In ( cosh (5v)) –· tanh 2(5v) 2 derivative of y with…

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Q: 1+ cos x y = In 1-cos x

A: This question is based on chain rule differentiation.

Q: B. By using the definition of the derivative, find the for: dx 1- f(x) = V %3D 2- f(x) = x -!

A:

Q: Find the second derivative 1. y = In(x^3+1) 2. y = Arctan (e^x)

A: Given: y=lnx3+1, y=tan-1ex

Q: 1 log3(r – y)*

A: Given; fx,y=1log3x-y   As we know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x And…

Q: (3e)® arctan (3x³) In(e2«) arccos(5x) 1. Find the derivative of f (x)

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Q: 2. S- x²+1 dx x3+3x

A:

Q: The antiderivative of the function sin (Gx+7) is:

A: Given : sin12x+7

Q: Can you help me step by step with this problem?

A: Differentiate both sides w.r.t. x.And for addition we can apply the derivative separately on both…

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Q: If y- sin x and yn) means "nth derivative of y with respect to x", what is the smallest posilive…

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Q: Find the differential for y = tan 2x2

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Q: Find the linear approximation of f(x)=lnx at x=1and use it to estimate ln⁡(1.3) L(x)=? ln 1.3≈?

A: First find the linear equation at x=1  then find the approximate values

Q: I FIND THE SECOND DERIVATIVE(y") OF THE FF IN ITS SIMPLIFIED FORM 2. Y= 2 Arccos (1-)+ v4x – x?

A:

Q: Solve for the derivative of the given implicit functions. a. Find dy/dx for y= ln (4x+tan-1(lnx)).…

A: Solve: a. Find dy/dx for y= ln (4x+tan-1(lnx)). b. Find dy/dx for y= tan-1 (3x-2 sinx). c. Find the…

Q: Find the differential of y=xsinπx2 at the point x=12 when dx=0,01.

A: We will use product rule and chain rule to find dy/dx

Q: I FIND THE SECOND DERIVATIVE(y") OF THE FF IN ITS SIMPLIFIED FORM 3x-4 1. Y= Arctan

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Q: Compute the second derivative with respect to r of 3x + 8 y = at x = 1.

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Q: c. Find the derivative of y =+- et x3 cOS X 2

A: