What is the differentiation of \(e^{sinx}\) ?

Solution :

Let y = \(e^{sinx}\). Putting u = sinx , we get

y = \(e^u\) and u = sinx

\(\therefore\) \(dy\over du\) = \(e^u\) and \(du\over dx\) = cosx

Now, \(dy\over dx\) = \(dy\over du\) \(\times\) \(du\over dx\)

\(\implies\) \(dy\over dx\) = \(e^u\)cosx = \(e^{sinx}\)cosx

Hence, the differentiation of \(e^{sinx}\) with respect to x is \(e^{sinx}\)cosx.