Question

Найти производную: 1) f(x)=tg(x+pi/4)
2) f(x)=sin2x+tgx
3) f(x)=4-1/4tgx
4) f(x)=x^2ctgx

Answer 1

1.

$f'(x) = \frac{1}{ { \cos }^{2} (x + \frac{\pi}{4}) } \\$

2.

$f'(x) = 2 \cos(2x) + \frac{1}{ { \cos}^{2} x} \\$

3.

$f'(x) = (4 - \frac{1}{4tgx} ) '= - \frac{1}{4} \times ( - {tg}^{ - 2} x) \times \frac{1}{ { \cos }^{2}x } = \\ = \frac{1}{4} \times \frac{ { \cos }^{2}x }{ { \sin }^{2}x } \times \frac{1}{ { \cos }^{2} x} = \frac{1}{4 { \sin }^{2} x}$

4.

$f'(x) = ( {x}^{2} )'ctgx + (ctgx) '\times {x}^{2} = \\ = 2xctgx - \frac{ {x}^{2} }{ { \sin }^{2} x}$