f(f (x)) and g (x) = f (x2). Use the 56. If fis the function whose graph is shown, let h (x) graph of f to estimate the value of each derivative. a. h' (2) b. g (2) y=f(x)

Q: Find the derivative of the function. Simplify where possible. f(x)   = x In(arctan x)

A: Given: The above function contains two functions, so the product rule is used to differentiate.

Q: Find the derivative of the function.

A: Given: To find: Derivative

Q: fex)=Dx3+ x + xs+3

A: We have to find

Q: Find the derivative. g(x) = tanh-1(x?)

A:

Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

A: Here the given function  hx=x+2, c=-2 The function can be written as hx=x+2,x≥-2-x-2,x≤-2

Q: Find the derivative of function.

A: The given function is f(x) = ln(xex+2).We have to find the derivative of this function with respect…

Q: Find the derivative of the function. g(x) = arccos(x) / x+7   g'(x)=__________________

A:

Q: B. By using the definition of the derivative, find the for: - dx f(x) = x -

A: Explanation of the answer is as follows

Q: f(x) = Arctan csc² ( 3x

A: Some derivative formulae: ddxtan-1x=11+x2ddxcscx=-cscx cotx Chain rule of derivative:…

Q: Find the derivative of f(x) = (Cosx)*

A:

Q: Determine the derivative of f(x) =2x/x2+1 using the quotient rule and find the equation of the…

A:

Q: Determine the derivative of f(x)=ln(x√x^2+1).

A:

Q: Find the derivative of the function: f(x) = ln X x+1* Is there a shortest way? Please explain.

A: We can find the answer in the following steps.

Q: Q1. Find the derivative of f(x) = 2x -- by using the definition of derivative.

A:

Q: 13. f(x) = e* In x

A:

Q: Find the derivative of the function. h(x) = x2 arctan(5x)

A: Given function: hx=x2tan-15x Differentiate the above function w.r.t "X" h'x=ddxx2tan-15x

Q: f (x) = ln(x · 5*)

A:

Q: Suppose that the SECOND DERIVATIVE of a function f is given by f" (x) = (x – 2)² (x² – 4x). Find the…

A:

Q: Find the derivative of f(x)=arctan(1/x) and simplify

A:

Q: Find the derivative using the Four-step rule f(x)=x/1-x

A:

Q: Find the derivative of f(x)= xtan(x)

A:

Q: fcx)= Y文 メ ー^

A: Local extrema

Q: Find the derivative of the function. 10 f(x) = 3 + 2cos x

A: Recall: dxndx=n xn-1 d(cos ax)dx= a(- sin ax) dc1f(x)±c2 g(x) dx= c1d[f(x)]dx± c2d[g(x)]dx

Q: Find the 4th derivative of the function y=exsinx.

A:

Q: The second derivative of the function is y = arctan 2x

A:

Q: Find the relative extrema of the function f(x)= x2+3x+4 using first derivative test.

A: fx=x2+3x+4 To find extrema of function.

Q: Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.

A: Consider the given: The numerical derivative does not exist a point in three cases: 1) when there is…

Q: Suppose that the second derivative of the function y = ƒ(x) is y′′ = (x + 1)(x - 2). For what…

A: For inflection point we must have y" = 0

Q: Find the derivative (x) = 2 In x – Vĩ

A: Given: fx=2lnx-x   As we know that; The sum/difference rule:  f±g'=f'±g' The Power law; ddxxn=nxn-1…

Q: Find the derivative of the function. f(x) = arctan(3x)

A: We  can make it easier for you.

Q: Find the derivative of y = arctan² (x³)

A: This is a problem of differentiation of the function. Based on general formula we will solve this…

Q: Find the 4th derivative of x^10 evaluated at x=0. What would be the 100th derivative of x^2000 be at…

A:

Q: Find the derivative of the function. f(x) = 4 3√x + 2cos x

A: The given function is ; f(x)=4/3sqrt(x) +2Cosx.

Q: Find f′(x) from f(x)=2x^3−x^2−x+2 using the definition of a derivative. (Do not include "f′(x)=" in…

A: we have to find f'(x) using limit definition of derivative

Q: Find the derivative of the function. g(x) = 9 + In(x)

A: We have to find the derivative of : g(x)=ex29+ln(x)

Q: Find the derivative. f(x) = 2^x {ln[cot(x)]}^2

A:

Q: Use a quick approximation to estimate the derivative of the given function at the indicated point.…

A: f (x) = 1 − 2x  point,  x = 2 To use quick approximation to estimate the derivative, f'(2).

Q: Find the derivative of the function. g(x) = 2(3- Ex)

A:

Q: 9. Use the definition of a derivative change of the functions below at f(x)% = x² + 2x

A:

Q: 14. Find the derivative of the function using the definition of derivative. f (x) = V1 – x

A: Derivatives

Q: find the derivative of y with respect to the appropriatevariable. y = csch-1 2θ

A: Given, y=csch-12θ

Q: the derivative of f(x) = xi at the point x = 4?

A:

Q: By using first principle, show that the derivative of f(x)=- is x+1 1 S'(x) = (x+1)

A:

Q: Find the derivative. Simplify where possible. y  = x tanh-1 x   + In √ (1- x2)

A: We have given that, y=xtanh-1x+ln1-x2 We have to find the Derivative of this function i.e. y' As we…

Q: Find the first derivative of the function below: f(x) = arctan(sec(x ))

A:

Q: Find all possible functions with the given derivative. = రx = 1x 2x

A: The answer is given below

Q: Find the derivative of the function. h(x) = x² arctan(8x)

A:

Q: 1. Use the definition of the derivative to find the derivative of f(x)- V-x-2

A:

Q: Find the derivative of the function. h(x) = ets. - x + 1

A: Differentiate w.r.t x

Q: Find the derivative of the given function by using definition of derivative  f(x)= sec(x)

A: