Answer the second question b) a) Let f(x)=tan-¹().-18ㅎFind f'(x) =-1b) Let g(x) = √64 — x² + 32 sin¯¹ (-Find g'(x) = -200

g(x)=x264-x2+32sin-1(x8)d dx(sin-1)=11-x2d dx(xn)=nxn-1d dx(x)=12xd dx(a.b)=adbdx+bdadx

Answered: b) Let g(x) = 2√√64 – x² + 32 sin¯¹…

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b) Let g(x) = 2√√64 – x² + 32 sin¯¹ Find g'(x) = 8|00

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.4: Definition Of The Derivative

Problem 6YT

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Q: a) Let f(x) tan-¹(²). -1 8 = ㅎ Find f'(x) = -1 b) Let g(x) = 2√√64 – x² + 32 sin Find g'(x) = - 200

Question

Answer the second question b)

a) Let f(x)
=
tan-¹().
-1
8
ㅎ
Find f'(x) =
-1
b) Let g(x) = √64 — x² + 32 sin¯¹ (-
Find g'(x) = -
200

Expert Solution

Step 1

$g (x) = \frac{x}{2} \sqrt{64 - x^{2}} + 32 \sin^{- 1} (\frac{x}{8}) \frac{d}{d x} (\sin^{- 1}) = \frac{1}{\sqrt{1 - x^{2}}} \frac{d}{d x} (x^{n}) = n x^{n - 1} \frac{d}{d x} (\sqrt{x}) = \frac{1}{2 \sqrt{x}} \frac{d}{d x} (a . b) = a \frac{d b}{d x} + b \frac{d a}{d x}$

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