Question

Помогите найти производные

Answer 1

16)
$y=cos(5^x+1) \\ y'=-sin(5^x+1)*5^x*ln5$

17)
$y=tg^2(3x) \\ y'= \frac{6tg(3x)}{cos(3x)} = \frac{6sin(3x)}{cos^2(3x)}$

18)
$y=ln(2+3^{2x}) \\ y'= \frac{3^{2x}*ln3*2}{2+3^{2x}}$

19)
$y=sin^4(2x+1) \\ y'=4sin^3(2x+1)*cos(2x+1)*2=4sin^2(2x+1)*sin(4x+2)$

20)
$y=\sqrt{4sin(2x)+x} \\ y'= \frac{8cos(2x)+1}{2\sqrt{4sin(2x)+x}}$

21)
$y=cos^3(x^2+2x) \\ y'=3cos^2(x^2+2x)*(-sin(x^2+2x))*(2x+2)=\\=-6(x+1)*cos^2(x^2+2x)sin(x^2+2x)$