Question

Find the derivative of the following function. $y = \frac{1}{6 + 5\sin x}$ $\frac{dy}{dx} = \square$

Name: find the derivative of the following function y frac16 5sin x fracdydx square 22829
Uploaded: 2024-04-14T05:01:04-08:00
Duration: 1 min 25 s
Channel: Taha T
Description: find the derivative of the following function y frac16 5sin x fracdydx square 22829

          Find the derivative of the following function.
$y = \frac{1}{6 + 5\sin x}$
$\frac{dy}{dx} = \square$

$find the derivative of the following function y frac16 5sin x fracdydx square 22829$

Added by Kelli C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Taha T

04/14/2024

Step 1

We use the chain rule to find the derivative. The chain rule states that if $y = f(g(x))$, then $\frac{dy}{dx} = f'(g(x))g'(x)$. In this case, $f(u) = u^{-1}$ and $g(x) = 6 + 5\sin x$. Then $f'(u) = -u^{-2}$ and $g'(x) = 5\cos x$. Show more…

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