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Question

If f(1)=1,f(1)=3, then the derivative of f(f(f(x)))+(f(x))2 at x=1 is :

A
9
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B
12
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C
15
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D
33
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Solution

The correct option is D 33
Let y=f(f(f(x)))+(f(x))2
dydx=f(f(f(x)))f(f(x))f(x)+2f(x)f(x)
dydxx=1=f(f(f(1)))f(f(1))f(1)+2f(1)f(1)
=333+213=33

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