Question

Знайти похідну функції


1) f(x)=x^7ctgx


2)f(x)=x^2cosx


3)f(x)=x^5sinx

Answer 1

Ответ:

1

$f'(x) = (x {}^{7} )'ctgx + (ctgx) '\times {x}^{7} = 7 {x}^{6} ctgx - \frac{ {x}^{7} }{ \sin {}^{2} (x) }$

2

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

3

$f'(x) = ( {x}^{5} ) '\sin(x) + ( \sin(x))' \times {x}^{5} = 5 {x}^{4} \sin(x) + {x}^{5} \cos(x)$