Find f'(x). f(x) = e\ – x³ arctan(x) f'(x) = %3D Check that your answer is reasonable by comparing the graphs of fand f'. f' = 0 where the graph of f has a horizontal tangent. f'is negative when f is-Select-- f'is positive when f is -Select---

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A: Differentiate the cosh3x2y=lnexy+1 with respect to x. dcosh3x2ydx=dln(exy+1)dx Use the chain rule…

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Q: Find 3rd order derivative of y with respect to x , if x = a sint, y = b cost.

A: Given: x = a sint y = b cost -------------------------------------------------- To find: 3rd order…

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A: Derivative of a function implies the rate of change of that function.

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Q: 2. Use implicit differentiation to find tangent at the given point: (a) xy + y² = 3-3x² at (-1,1).…

A: use implicit differentiation, I try to provide typed solution, if it is helpful like it.

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Q: I. Find an equation of the tangent line to the graph of t cosh (f² – 1) dt tan-l † | f(x)%3D /1+ln…

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Q: b. y = cosh(arctan 3x)

A: Given: y=coshtan-13x We know that ddxcoshx=sinhx                                              ..1

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A: Aim: We have to differentiate given function.

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Q: Calculate the derivative of y=arctan√ex at x=0.

A: We differentiate both sides with respect to x using the chain rule.

Q: 1 at x= 4 by using the 2Vx Q2. Find the slope of the tangent line to the function f(x)= definition…

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Q: implicit derivative to find dy/dx of    xy + arcsin(y)+2^y=ln(x)

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Q: = Determine the equation of the tangent line to the graph of f(x) = I x+ln x cosh (√2t - 1) dt at x…

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Q: It can be shown that the Difference Quotient (D.Q.) of f (x) = sinx is h-[sinx(cos(h) – 1) +…

A: We are provided that the Differential Quotient (D. Q.) of f(x)=sinx is h-1sinxcosh-1+cosx sinh, if…

Q: Use Richardson extrapolation to find an improved estimate for the first derivative of y = cos x at x…

A: Solution: The given function y=cosx We have to use Richardson extrapolation at x=π4 Using steps…

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Q: Use implicit differentiation to find dy/dx X^3+ sin y=x^2 y^5

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Q: What is the second derivative of ecON (), , Cosh (A sinh?(x)e cosh (x) + cosh2(x)ecosh («) B sinh…

A: Let the given function is y=ecosh(x).

Q: y = In(x² + 4) - x tan-1 (e) y = arctan(arcsin vx), (y = sech (tanh x)

A: NOTE: Refresh your page if you can't see any equations. . take derivative

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Q: The average rate of change of the function y = sinx over the interval [0, ]is 4

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Q: Find the derivative of the function g(x) = (arctan x)³, first showing how to get the formula for -…

A: Consider the function  g(x)=tan−1x3

Q: Find all values 197. gh of aci on the the graph of f(x) = -3 sinxcosx where the tangent line is…

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Q: Sin 4x-Sec?x) dx =?

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Q: Differentiate y= arctan sinh x. coshx A. 1-sinh x cosh x B. cosh x C. ainh-x D. 1+sinh-x

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Q: 7) Find the average rate of change of the function A(x) = sin ( 2x - -) from x = to x =

A: A(x) = sin(2x - π/6) A(x2) = A(5π/6)          = sin(2*5π/6  - π/6)          = sin (9π/6)          =…

Q: Find the derivative of the function. f(x) = In(sinh(x)) %3D f '(x) = %3D

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Q: 1. [cosh(x)] = sinh(x) dx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find all points with x-values on (0, 2π), where tangent line to the graph of f(x) is horizontal.…

A: Find all points with x-values on (0, 2π), where tangent line to the graph of f(x) is horizontal.…

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Q: 9 y = Arctan(+x, 1- 2x

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Q: Calculate the derivative of the function y=arccos x arctan x at x=0.

A: Differentiating with respect to x, we get

Q: Find all x values on the graph of f(x) = - 3 sin x cos x where the tangent line is horizontal.

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Q: a Write down the derivative of arcsinx. b Use integration by parts to find | arcsinx d.x.

A: a. Derivative of arcsin(x) is given by ddx(arcsin(x)) = ddx(sin-1(x)) = 11 - x2

Q: Find the derivative of y with respect to x.   y= tan-1 *square root (16x2-1) +csc-1*4x ,   x greater…

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Q: Determine the equation of the tangent line to •x³ +ln x the graph of f(x) at x = 1. [² = √/3 + 5t5dt

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Q: -1/16 dx =

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