คำตอบ - Derivative

Computing the derivative of a cosine function using the chain rule.

$$\frac{d}{dx}\left[\cos \left(e^x\right)\right]=-\sin \left(e^x\right)\times \frac{d}{dx}\left[e^x\right]$$

Decomposing the function for the chain rule.

$$\frac{d}{dx}\left[\cos \left(e^x\right)\right]=\frac{d}{dx}\left[\cos \left(x\right)\right]\times \frac{d}{dx}\left[e^x\right]$$

Computing the derivative of a cosine function.

$$\frac{d}{dx}\left[\cos \left(x\right)\right]\times \frac{d}{dx}\left[e^x\right]=-\sin \left(x\right)\times \frac{d}{dx}\left[e^x\right]$$

Substituting the variable back into the function.

$$-\sin \left(x\right)\times \frac{d}{dx}\left[e^x\right]=-\sin \left(e^x\right)\times \frac{d}{dx}\left[e^x\right]$$