Exercise 2: Derive the formula for the derivative of arcsec(x) in two different ways: (a) Let arcsec(x) sec(y). Then solve for the derivative as an inverse function in our usual = Y, so x = you will have to be careful with the positive and negative signs. Note way. (b) Show that arcsec(x) = arccos(1/x). Then differentiate arccos(1/x) via the chain rule.

Q: Find the derivative of each function. A. f(x) = x2 - sinx + B. g(x) = (x² + 1) cosx %3D

A: Given that 1. A. fx=x2-sinx+1x3B. gx=x2+1cosxTo find : DErivative of functionSolution A.…

Q: Does the function cos x х f(x) = 0, x = 0 have a derivative at x = 0? Explain.

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Q: Find the derivative of the function.

A:

Q: Derive the formula for the derivative with respect to x of csc x.

A: We will write cscx= 1/sinx  Then we will use the quotient rule to differentiate

Q: Question * The derivative of the function f(x)= 2x² + tan x + 3e* is:

A:

Q: Use logarithmic differentiation to find the derivative of the function y = Vi e* (x² + 1)'. y = %3D

A: In logarithmic differentiation you need to first take log of both the side and then start…

Q: Define the second derivative of f. If f(t) is the position  function of a particle, how can you…

A: Second derivative is derivative of the derivative.      Therefore,…

Q: What is the Derivative of the function; y=tan\sqrt{x2-1}

A: Given function is y=tanx2-1. To find the derivative of the function. Solution: Chain rule of…

Q: Evaluate the derivative of the function. y= sec "(2 In 8x) dx

A:

Q: Find the derivative of f(x) = arcsin 2

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Q: In Exercises 33–46, find the derivative.

A: According to the question,we have to find the derivative of y=arctan x3 or it can be written as…

Q: • y= cos(a' + x')

A:

Q: Sketch the graph of a function z = f(x, y) whose derivative fx is always negative and whose…

A: Given that z=f(x, y) fx is always negativefy is always positive

Q: Find the 75th derivative of y=cos(2x)

A: Given function y=cos2x The 75th derivative has to be founded  first consider the smaller…

Q: Find the derivative. y = arcsech V1 - x2 ), x > 0 y' =

A:

Q: Find the derivative of the function. f(x) = sin-(4x) f'(x) = %3D

A: The given function is: f(x)=sin-1(4x) To find f'(x) here.

Q: Find the derivative of the function.

A: Given: g(x)=arcsin(3x)x

Q: Question * The derivative of the function y = x(tan¬1(3x))² is:

A:

Q: What is the third derivative of f (x) = a + cosæ?

A:

Q: . Does the function cos x x + 0 f(x) = 0, x = 0 have a derivative at x = 0? Explain.

A: Consider the given function fx=1-cosxx        x is not equal to 0x=0

Q: Find the derivative of cos (x/y)

A:

Q: use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y =…

A: given y=cos9θ+41

Q: Compute the derivative.

A: Given function is Here, we use product rule of differentiation to find f'(x)

Q: Use logarithmic differentiation to find the derivative of the function. y=cos(3x)^x

A: The given function is y=(cos(3x))x

Q: (a) Find the derivative of the function g(x) = sin2 x + cos2 x (b) then use a trigonometric…

A:

Q: Find the derivative of the function. "1(* - VI + x) y = 9 tan

A: derivative

Q: Compute the derivative of f(x) = arcsin(x? e

A: Given f(x)=sin-1(x2e3x)

Q: Use logarithmic differentiation to find the derivative of the function. y = x4 cos(x) y' = || %3D

A: y = x4cosx take both side natural log lny = 4cosx(lnx) now differentiate with respect to x (y')/y =…

Q: Find the derivatives of the functions in Exercises y = 2 tan^2 x - sec^2 x

A: y=2 tan2x-sec2x

Q: -1 2.) у %3D tan -6.x4

A: To differentiate: y=tan-1(-6x4) Solution: We know, ddx(f(g(x)))=f'(g(x)).g'(x)…

Q: Find the derivative of the function. f(x) = sin (4x) %3D

A: To find the derivative of the function.fx=sin-14x

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. (t - g'(s)…

A:

Q: Find the derivative of f(x) = tan -(e*) %3D

A: Derivatives of some functions are given below.

Q: Determine the second derivative of the function y=arcsin x2−1 / x2+1.

A:

Q: Find the derivative of each function. a) f(x) = b) y = tan-(23x² + 4x – 2) sec-1(x³) c) y = V1– x²…

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

Q: Find the derivative. f (x) = e* COS X %3D

A:

Q: f(x) = log,(x² – x + 3)

A: Given: f(x)=log4(x2−x+3)

Q: Find the 42nd derivative of the function y=sin(x).

A:

Q: Use logarithmic differentiation to find the derivative of y. y= cos X-3x + %3D

A: We can find the derivative using logarithmic differentiation as below.

Q: Solve for the derivative of the Inverse Trigonometric Differentiation.  1.  g(x) = 3 tan -1 (3x)…

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Q: In Exercises 33–46, find the derivative.

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Q: Compute the derivative of f(x) = arcsin(x² e3=).

A:

Q: Find the derivative of  f(x) = tan(cos(x^2))

A: f'(x) = d (tan(cos x2)dx  f'(x) = sec2(cos(x2))d cos x2dx               because   d (tan(x))dx =…

Q: Derive the formula for the derivative with respect to x of a. sec x.      b. csc x.           c. cot…

A:

Q: Use a computer algebra system to find the derivative of the function.

A: Given

Q: Solve for the derivative of the function using chain rule. 6. f(x)= cot(6x3+5)

A: Derivative

Q: Compute the derivative of f (x) : = arcsin(x² e³«).

A:

Q: In Exercises 33–46, find the derivative.

A: To find the derivative

Q: EXERCISE 3. Derive a formula for the nth derivative of f(x)

A: