Question

Encontre as derivadas das funções:

ce826b2aa17278be74ae4b50ab6fbd94.pdf

Answer 1

Oi Andreia :) 

Aí estão as derivadas das funções. 

a)
$y=x^8+x^7-x \\ \\ y'=8x^7+7x^6-1$

b)
$y=3x^{-4}-5x \\ \\ y'=-12x^{-5}-5$

c)
$y=(x+1)(3x-2)(5x+1) \\ \\ y=(3x^2-2x+3x-2)(5x+1) \\ \\ y=15x^3+3x^2-10x^2-2x+15x^2+3x-10x-2 \\ \\ y=15x^3+8x^2-9x-2 \\ \\ y'=45x^2+16x-9$

d)
$y= \frac{x^2-3x}{x^3+5} \\ \\ y'= \frac{(x^2-3x)'(x^3+5)-(x^2-3x)(x^3+5)'}{(x^3+5)^2} \\ \\ y'= \frac{(2x-3)(x^3+5)-(x^2-3x)3x^2}{(x^3+5)^2} \\ \\ y'= \frac{2x^4+10x-3x^3-15-3x^4+9x^3}{(x^3+5)^2} \\ \\ y'= \frac{-x^4+6x^3+10x-15}{(x^3+5)^2}$

e)
$y= \frac{x^{-3}+x^2}{x^{-5}+3x^7} \\ \\ y= \frac{(x^{-3}+x^2)'(x^{-5}+3x^7)-(x^{-3}+x^2)(x^{-5}+3x^7)'}{(x^{-5}+3x^7)^2} \\ \\ y'= \frac{(-3x^{-4}+2x)(x^{-5}+3x^7)-(x^{-3}+x^2)(-5x^{-6}+21x^6)}{(x^{-5}+3x^7)^2} \\ \\ y'= \frac{-15x^{18}-30x^{13}+7x^6+2x}{(3x^{12}+1)^2}$