Question

A derivada primeira de : f (x) = x5 – 2x3 + x:

Answer 1

$\large\boxed{\begin{array}{l}\underline{\sf Regras\,b\acute asicas\,de\,derivac_{\!\!,}\tilde ao}\\\rm 1)~\dfrac{d}{dx}[k]=0,sendo\,k\,constante\\\\\rm 2)~\dfrac{d}{dx}[f(x)\pm g(x)]=\dfrac{d}{dx}f(x)\pm\dfrac{d}{dx}g(x)\\\\\rm 3)~\dfrac{d}{dx}[f(x)\cdot g(x)]=\dfrac{d}{dx}f(x)\cdot g(x)+f(x)\cdot\dfrac{d}{dx}g(x)\\\\\rm 4)~\dfrac{d}{dx}\bigg[\dfrac{f(x)}{g(x)}\bigg]=\dfrac{\dfrac{d}{dx}f(x)\cdot g(x)-f(x)\cdot\dfrac{d}{dx}g(x)}{g(x)^2}\\\\\rm 5)~\dfrac{d}{dx}[u^n]=nu^{n-1}\cdot\dfrac{du}{dx}\end{array}}$

$\large\boxed{\begin{array}{l}\rm f(x)=x^5-2x^3+x\\\rm f'(x)=5x^4-6x^2+1\end{array}}$