Chapter 4] If f(x) = dt, where g(x) = 1," (÷) V1+t3 [1 + sin(t²)] dt, find f'

Q: Q2/ A/ Show that the functions f(x) = sin-1() and g(x) = 2tan-Vx, have the same derivative. %3D

A: Given : f(x)= sin-1 ( x-1 / x+1 ) g(x) = 2 tan-1 (√x)

Q: Show that the derivative of FOx) =x² is f'x)=2x using the defimition

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Q: Find f.  f''(t)=sin t + cos t,    f(0)=2,    f'(0)=4f f(t)= ?

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Q: sin () (cos (t*) + t)dt %3D (2), NOTE: Enter a function as your answer. Make sure that your syntax…

A: In the given question, the Fundamental Theorem of Calculus Part I is applied. ∫afxgtdt=gfx·f'x

Q: Find f'(x) if f(x) = 1 (x+csda4+10))³

A: *concept:- cscx = 1/sinx. d/dx (sinx) = cosx. d/dx (x^{n}) = nx^{(n-1)}

Q: Find f'(2) if y = f(x) is the nonnegative function defined for x, y > 0 by the equation x" = y?.

A: To find f’ (2), if y = f (x).

Q: find f'la) f(x)%3D(X

A: The given function is: f(x)=x-1x2

Q: R(x)= 1 dt . 76 +4 Use FTC part II to find the derivative of the function

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Q: F’(-4)=

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Q: 7 (2+ x³)' Vx² – 1 (x2 + x + 1)* 3 d B : dx - 4

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Q: mula for the derivative of the inverse function of f?

A: We have given a function  f(x)=∫0x(1+sin(sin(t)))dt We have to find f-1'(0).

Q: Find the original function f(x) from given equation f'''(x)

A: We can solve this as follows:

Q: sin 0 r (0) = log„(ršin ® – sin" 0)

A: We know that, from the derivative formulas ddxax=axloga       ⋯⋯1ddxlogx=1x…

Q: what does f'(m)= ?

A: We need to provide meaning of f'(m).

Q: Find the inverse function of f(z) = 4 + V7. f"(z) =

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Q: Find f', given f'(x) = f(x) = x sin³ (25) √²+1

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

Q: 2) s(t)=5e" (3r -51)

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Q: What is f'(0)?

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Q: 8) Find the derivative of each function: 2. a)g(x) = 3x +5x

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