Question

Нужно найти производную функции: а)y=x(в шестой степени)б)y=2 в)y=5/x г)y=3-5x д)sinx/x е)y=x ctg x

Answer 1

$1) \ y=x^6\\ f'(x)=(x^6)'=6x^5\\\\ 2) \ y=2\\ f'(2)=0\\\\ 3)\ y= \frac{5}{x}\\\\ f'( \frac{5}{x})= \frac{5'\cdot x-5\cdot x'}{x^2}= \frac{0-5}{x^2} =- \frac{5}{x^2}\\\\ 4)\ y=3-5x\\ f'(3-5x)=3'-(5x)'=0-5=-5\\\\ 5)\ y= \frac{\sin x}{x} \\\\ f'( \frac{\sin x}{x})= \frac{(\sin x)'\cdot x-\sin x\cdot(x)'}{x^2}= \frac{x\cos x-\sin x}{x^2}\\\\ 6)\ y=xctg x\\ f'(xctgx)=x'\cdot ctgx+x\cdot(ctgx)'=ctgx- \frac{x}{\sin^2x}$