Suppose f(x)=(2^x+2^-x) x ^-1(x^2-x+1)(7x^2+3x+1)^3.

Question

Suppose $f(x)=\frac{({2}^{x}+{2}^{-x})	an x\sqrt{{	an }^{-1}({x}^{2}-x+1)}}{{(7{x}^{2}+3x+1)}^{3}}$. Then the value of ${f}^{'}(0)$ is equal to

Accepted Answer

$\begin{gathered} {f}^{'}(0)=\underset{h	o 0}{lim}\frac{f(h)-f(0)}{h} \ =\underset{h	o 0}{lim}\frac{({2}^{h}+{2}^{-h})	an h\sqrt{{	an }^{-1}({h}^{2}-h+1)}-0}{{(7{h}^{2}+3h+1)}^{3}h} \ =\sqrt{\pi } \end{gathered}$

Solutions · 1