Paragraph: Let f:(-1,1) R be a differentiable function with f(0)=-1 and f^ (0)=1 . Let h(x)=f(2 f(x)+2) and g(x)=(h(x))^2 . Question: What is h ^ (0) equal to?

Step-by-step solution

Let f :(-1,1) R be a differentiable function with f (0)=-1 and f^ (0)=1h(x)=f(2 f(n)+2) Differentiate both side w.r.t x aligned & h^ (x)=f^ (2 f(x)+2) 2 f^ (x) & h^ (0)=f^ (2 f(0)+2) 2 f^ (0)=f^ (-2+2) 2(1) & =f^ (0) 2=(1) 2=2 [ f(0)=-1 and f^ (0)=1 ] aligned