Question

Find the second derivative, do not have to simplify

Answer 1

`f(x)=\sec(\pi x)=(1)/(\cos(\pi x))=[\cos(\pi x)]^(-1)\\\\\text{use}\\\\(a^n)'=na^(n-1)\\\\(\cos x)'=-\sin x\\\\f'(g(x))=f'(g(x))\cdot g'(x)`

`f'(x)=\left\{[\cos(\pi x)]^(-1)\right\}'=-[\cos(\pi x)]^(-2)\cdot[-\sin(\pi x)]\cdot\pi\\\\=(\pi\sin(\pi x))/([\cos(\pi x)]^2)=\pi(\sin(\pi x))/(\cos(\pi x))\cdot(1)/(\cos(\pi x))\\\\=\pi\tan(\pi x)\sec(\pi x)`