Question

Нужно найти пройзводную........
1)y=(x^3+x^-2+11)^3=?
2)y=sin(5x-3)=?​

Answer 1

1)

$y'=((x^3+x^{-2}+11)^3)'=3\cdot (x^3+x^{-2}+11)^2\cdot (x^3+x^{-2}+11)'=\\\\=3\cdot (x^3+\frac{1}{x^2}+11)^2\cdot (3x^2-2x^{-3}+0)=\frac{3\cdot (x^5+1+11x^2)^2}{(x^2)^2}\cdot (3x^2-\frac{2}{x^3})=\\ \\ = \frac{3\cdot (x^5+1+11x^2)^2}{x^4}\cdot (\frac{3x^5-2}{x^3})=\frac{3\cdot (x^5+11x^2+1)^2\cdot (3x^5-2)}{x^7}$

2)

$y'=(\sin{(5x-3)})'=\cos{(5x-3)}\cdot (5x-3)'=5\cos{(5x-3)}$