Question

Найдите производную функции:
a). $y=x^2+x^3$
b). $y=x^7-x^3$
c). $y=4x^5-2$
d). $y=-5x^3+4$
e). $y=frac{1}{x}(2x+1)$
f). $y=frac{1}{x}(x^6-5)$
g). $y=(1-x^{20})frac{1}{x}$

Answer 1

$y=x^2+x^3;\ y'=2x+3x^2;$

$y=x^7-x^3;\ y'=7x^6-3x^2;$

$y=4x^5-2;\ y'=20x^4$

$y=-5x^3+4;\ y'=-15x^2;$

 

$y=frac{1}{x}(2x+1)=2+frac{1}{x};\ y=-frac{1}{x^2}$

 

$y=frac{1}{x}(x^6-5)=x^5-frac{5}{x};\ y'=5x^4+frac{5}{x^2}$

$y=(1-x^{20})frac{1}{x}=frac{1}{x}-x^{19};\ y'=-frac{1}{x^2}-19x^{18}$