2. If f"(x) = 4sinx+16cosx, f(0) = 6, f'(0) = 1, find f(x) and f(4).

Q: dy/dx if y=tan((1-2x)/(1+x)) dy/dx if y=x^4 ln(3x-1)

A: 1)    y=tan1-2x1+x2)    y=x4ln(3x-1) Hint:  Chain rule and then uv and u/v rule of differentiation

Q: If z = +3y, find the differential dz. dz =

A:

Q: Find the differential of the function y=√x3+4x at x=2.

A: Given the function:

Q: OFind the second derivative of y = 4Vx + E + 10

A:

Q: Let y=(x2+3) to the 2nd power. Find the differential dy when x=4 and dx=0.2 ?????????? Find the…

A:

Q: 2. Calculate the derivative of the following. А. y = (x* – 3x² + 5x) ³ DUKAS B. y = tan²(x² + 5x –…

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

A:

Q: 1. Find the rate of y with respect to x at the point (1,8) if 7y² - xy³ = 4. dy dx

A: Given: 7y2-xy3=4 and Px,y=1,8   As we know that; The Power Law: ddxxn=nxn-1 The Product rule:…

Q: What is the derivative 7 of y = (3x + 1)²? 21 dx dy = 6 (3x + 1)²¹ dx = dy 6 (3x + 1)² dx = 7 (3x +…

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Q: 2. Find dy/dx by implicit differentiation: 5x^2y+5y^2x=-3

A:

Q: Find dy/dx in terms of x and y if cos^2(9y)+sin^2(9y)=y+7 dy/dx=   implicit derivative problem.

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Q: for (e3x+y2)5 = sin x cos y, find dy/dx. using implicit differentiation. must show all steps

A:

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

A: Given: x2+y2=81

Q: If y = 4x³ + 2x² + 11, find the approximate value of y when x = 2.01, using differentials.

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Q: 2 1 Estimate -dx using the right endpoint rule with n = 4 3 1+x

A:

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

A:

Q: - ((x3 + x)sech(In x)) = dx EX)-

A: To find  ddx(x3+x)(sech(ln x) We use product rule  d(uv)=udv+vdu Let  u=x3+x,     v=sech(ln…

Q: If f(x,y) = y2 ex + 3 ln (xy), find fxyy (1,1). fxyy (1,1) = ?

A:

Q: To use differentials to approximate V9. You would use x = and dx

A: Solis as follows

Q: If tan2(2y) – S cost dt = 4 - x² %3D dx

A:

Q: The derivative of y = 3cos(8x+6) is: 1. y' = 24 sin (8x+6) 2. y' = -24 sin (8x+6) 3. y' = -24 cos…

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Q: If y = sin (4x - 5), then what is y' a. y = 4 cos (4x - 5) b. y 3 сos (4x - 5) C. y' = -cos (4x) d.…

A: In this question  we have to solve the given statements. NOTE: As per our policy we are suppose to…

Q: # 5) Find the extrema points for the function f (x) = using the second derivative tes 1+x x2 %3D Fon…

A: To find the extreme points.

Q: Solve for the differential of y when y= sinzx. x= -, and dx 3 2 4

A: we have to solve the problem

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: Given the function f(x) = e-3x cos 3x, x = [0, 2π]. When is the rate of change of f(x) a maximum?

A: Here, the given function is: f(x)=e-3xcos(3x) Now, the rate of change is given by: f'(x)=e-3xddx(cos…

Q: 2. What is the average rate of change of the function f (x) = x² – 3x over the interval [1,1.01]?

A: use average rate of change formula .

Q: 8. Find dy/dx- y = sin (1 + x^2/1-x^2)

A: I have stated the used formulas in the solution

Q: 11. Sds 3 ex+2 cos x-sin x 12. S -dx cos2 x

A:

Q: (a) By using the chain rule and the derivative = (xl) if x>0 (-1, if x< O' dx find - (Ix – x|)DvxE…

A: Given : ddx(x)=1 ,     if x&gt;0-1 , if x&lt;0 To find : ddx(x3-x) , where x∈(-1,1) and x≠0

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…

Q: 19. What is the derivative, of the function, dx dy y = 3x2 + 6x – 4 + 2e* – 3ln x А. dy 3 32x + 6 –…

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Q: (a) By using the chain rule and the derivative if x>0 (1, -1, if x< O' d (\xl) = dx | d find - (lx3…

A: Just break the mod function in two parts and easily calculate the derivative.

Q: 2. Approximate the derivative of f(x) forward, backward, and central difference method and step size…

A: To obtain the derivative at the point x0,y0, the following methods can be used:- The forward…

Q: Whatis the derivative of y = sin (2x − 1)? dx = 2 cos (2x - 1) dy dx = cos 2x dy -2 cos (2x - 1) cos…

A:

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 INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: (x2-3x)3 ; d'y/dx 1. y = 2. Y = (7x + 2)5…

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Q: 15 - What is the approximate derivative of f(x) = 5x³ + 4x² if we use f(ze+h)–f(za) forward…

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Q: y is a function of  x and the slope of the function is zero at x=10 then to determine that y reaches…

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Q: 1. If f(x, y) = sin(4x-2y)+ln(x²-2y) find fy fyx

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Q: (4)The instantaneous rate of change of f(r) = e- at a = 1 is . .. (5) The derivative of f(x) = sec2…

A: (4) We have So we get the instantaneous rate of change of the function at  as .

Q: Evaluate the integrals

A: Given integral is:

Q: 2 e -8; x(0) = 1 dt

A: Solution is given below:

Q: 1. If f(2) = 1, find the constant of integration for dx f(x) = +3

A:

Q: 4. Find the Linearization of f (x) sinx at a Provide your answer as L(x) =?

A: The given problem is to find the linearization of the given function at given point. Given…

Q: What is derivative d(y)/d(x) of "xsin(1/y^e)=(1-xy²)^½

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Q: Find the first derivative 1. y = In v4-x2 %3D 2. In(x2 + y2) + 4arctan = 5 y %3D dy x+4 3. Find , if…

A: