find the derivative of f(x).\n( f(x)=sin (-2 x+5) )\n( 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))