left f(x)=2^(sin(x)) Find f'(x)

Question
left \(f(x)=2^(sin(x))\)
Find f'(x)

Answers (1)

2021-02-10
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)
\(=2^uIn(2)cosx\)
\(=(In2)2^(sinx)(cosx)\)
0

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