Question

Obter a derivada das funções a seguir:

1) f(x)=10
2)f(x)=x^5
3)f(x)=10x^5
4)f(x)=1/2 x^2
5)f(x)=x^2+x^3

Answer 1

$\displaystyle1)\frac{df}{dx}=0\\\\2)\frac{df}{dx}=5x^{5-1}=5x^4\\\\3)\frac{df}{dx}=5.10x^{5-1}=50x^4\\\\4)\frac{df}{dx}=\frac{1}{2}\frac{d}{dx}(x^2)=\frac{1}{2}2x^{2-1}=\frac{1}{2}.2x=x\\\\5)\frac{df}{dx}=2x^{2-1}+3x^{3-1}=2x+3x^2$