Question

derivada de y= cos pi x+1/ x

Answer 1

$y=\dfrac{\cos(\pi x)+1}{x}\\ \\ \\ \dfrac{dy}{dx}=\dfrac{(\cos(\pi x)+1)'x-x'(\cos(\pi x)+1)}{x^2}\\ \\ \\ \dfrac{dy}{dx}=\dfrac{(\frac{d}{dx}\cos(\pi x)+1')-1\cdot(\cos(\pi x)+1)}{x^2}\\ \\ \\ \dfrac{dy}{dx}=\dfrac{(\frac{d}{d(\pi x)}\cos(\pi x)\cdot\frac{d(\pi x)}{dx})-(\cos(\pi x)+1)}{x^2}\\ \\ \\ \dfrac{dy}{dx}=\dfrac{(-\sin(\pi x)\cdot\pi)-(\cos(\pi x)+1)}{x^2}\\ \\ \\ \dfrac{dy}{dx}=\dfrac{-\pi\sin(\pi x)-\cos(\pi x)-1}{x^2}\\ \\ \\ \boxed{\dfrac{dy}{dx}=-\dfrac{\pi\sin(\pi x)+\cos(\pi x)+1}{x^2}}$