To compute the derivative of the given function (involving exponentials)

Step 2

Here ,we have used chain rule: If h(x)= p(q(x)), then h'(x) = p'(q) times q'(x)

Write \(f(x)=2^(u(x)),u(x)=sinx\)

by chain rule

\(f'(x)=(2^u)\)(derivative wrt u)*u'(x)

\(=2^uIn(2)cosx\)

\(=(In2)2^(sinx)(cosx)\)

Step 2

Here ,we have used chain rule: If h(x)= p(q(x)), then h'(x) = p'(q) times q'(x)

Write \(f(x)=2^(u(x)),u(x)=sinx\)

by chain rule

\(f'(x)=(2^u)\)(derivative wrt u)*u'(x)

\(=2^uIn(2)cosx\)

\(=(In2)2^(sinx)(cosx)\)