Differentiate e^cosx with respect to x.

To find: differentiation of e^cosx with respect to x

Let y = e^cosx

Taking log both sides:

⇒ log y = log(e^cosx)

⇒ log y = cos x log e

{∵ log a^x = x log a}

⇒ log y = cos x

{∵ log e = 1}

Differentiating both sides with respect to x:

Put the value of y = e^{cos x}:

Hence, differentiation of e^{cos x}with respect to x is –sin e^{cos x}