Question

Найдите производную функции: a). b). c). d). e). f). g). h). i). j).

Answer 1

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

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

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

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

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

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

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

$y=\frac{2}{x};\\ y'=-\frac{2}{x^2}$

$y=\frac{x-3}{x}=1-\frac{3}{x};\\ y'=-\frac{3}{x^2}$

$y=\frac{x+1}{\sqrt{x}}=\sqrt{x}+x^{-\frac{1}{2}};\\ y'=\frac{1}{2\sqrt{x}}- \frac{1}{2x\sqrt{x}}$