Question

Differentiate \[e^{\cos x}\] with respect to \[x\].

Options

• \[(\sin x)e^{\cos x}\]

• \[(\cos x)e^{\sin x}\]

• \[-e^{\sin x}\]

• \[-(\sin x)e^{\cos x}\]

Answer 1

Apply the chain rule to \[e^{\cos x}\]. The derivative of \[\cos x\] is \[-\sin x\], giving \[-(\sin x)e^{\cos x}\].