Question

find the derivative of f(x).
( f(x)=sin (-2 x+5) )
( f^{prime}(x)= )

Explanation:

Step1: Let \( u=-2x + 5 \)

Then \( f(x)=\sin(u) \)

Step2: Use the chain rule \( f^{\prime}(x)=\frac{df}{du}\cdot\frac{du}{dx} \)

First, find \( \frac{df}{du} \): \( \frac{d}{du}(\sin(u))=\cos(u) \)
Second, find \( \frac{du}{dx} \): \( \frac{d}{dx}(-2x + 5)=-2 \)

Step3: Substitute back \( u=-2x + 5 \)

\( f^{\prime}(x)=\cos(-2x + 5)\cdot(-2)=-2\cos(-2x + 5) \)

Answer:

\(-2\cos(-2x + 5)\)