Question

If $f(x) = \sin(x^5)$ then: $f'(x) = $ $f'(1) = $

Name: if fx sinx5 then fx f1 26967
Uploaded: 2023-11-21T06:12:22-08:00
Duration: 1 min 22 s
Channel: Zhumagali Shomanov
Description: if fx sinx5 then fx f1 26967

          If $f(x) = \sin(x^5)$ then:
$f'(x) = $
$f'(1) = $

Added by Carla D.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Zhumagali Shomanov

11/21/2023

Step 1

To find $f'(x)$, we need to use the chain rule. The chain rule states that if $f(x) = g(h(x))$, then $f'(x) = g'(h(x)) \cdot h'(x)$. In this case, let $g(u) = \sin(u)$ and $h(x) = x^5$. Then $f(x) = g(h(x)) = \sin(x^5)$. First, find the derivative of $g(u)$ Show more…

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