Question

найти производные, помогите пожалуйста​

Answer 1

Ответ:

1) $y = x^{ctgx^2} = e^{lnx*ctgx^2}\\y' = e^{lnx * ctgx^2}*(\frac{1}{x}*ctgx^2 + lnx * \frac{-1}{sin^2x} * 2)$

2) $y'_x = \frac{(t^5)'}{(t^3sint)'} = \frac{5t^4}{3t^2sint + t^3cost} = \frac{5t^2}{3sint + tcost}$

3) $y' = \frac{\frac{1}{(5x + 4)*\ln4} * 5 * ctg^4\frac{\pi}{x} - log_4(5x+4)*4*ctg^3\frac{\pi}{x} * \frac{-1}{sin^2\frac{\pi}{x}}  * \pi * (-1) * x^{-2}}{ctg^8(\frac{\pi}{x})}$

4) $y' = \frac{1}{\sqrt{1 - (\ln\cos\sqrt{3x})^2}} * \frac{1}{\cos\sqrt{3x}} * -\sin\sqrt{3x} * \frac{3}{2\sqrt{3x}}$

5) $y' = e^{\ln\sqrt{sin3x} * \frac{1}{\sqrt{x}}} * (\frac{1}{\sqrt{\sin3x}} * \frac{1}{2\sqrt{\sin{3x}}}*\cos{3x} * 3 * \frac{1}{\sqrt{x}} + \ln\sqrt{\sin3x} * \frac{-1}{2} * x^{\frac{-3}{2}})$