Mathematics, 05.07.2019 14:30 achimajdsjj
Find the second derivative, do not have to simplify
Answers: 1
![f(x)=\sec(\pi x)=\dfrac{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)](/tpl/images/0054/3835/51d44.png)
![f'(x)=\left\{[\cos(\pi x)]^{-1}\right\}'=-[\cos(\pi x)]^{-2}\cdot[-\sin(\pi x)]\cdot\pi\\\\=\dfrac{\pi\sin(\pi x)}{[\cos(\pi x)]^2}=\pi\dfrac{\sin(\pi x)}{\cos(\pi x)}\cdot\dfrac{1}{\cos(\pi x)}\\\\=\pi\tan(\pi x)\sec(\pi x)](/tpl/images/0054/3835/a91f3.png)
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