Question

Найдите производную:
$A) f(x)= x^{4} - frac{3}{x} + frac{1}{2} x^{2} - frac{1}{3} x^{3} ; B) f(x)= frac{cos3x}{x} ; C) f(x)= ( x^{2} + x sqrt{7} )^{7} .$

Answer 1

A)
f '(x) =(x⁴ -3/x +(1/2)*x² -(1/3)*x³ ) ' = 
(x⁴)' -(3*x^(-1))' +((1/2)*x²)' -((1/3)*x³)'=
4x³ -3*(-1)*x^(-2)  +(1/2)*2x -(1/3)*3x²=4x³ +3/x²  +x -x² .
B)
f'(x) =( (cos3x)/x ) ' =((cos3x)'*x -(x)'*(cos3x)/x²=
(-sin3x*(3x)'*x -cos3x)/x²= -(3x*sin3x +cos3x)/x².
C)
f '(x) =( (x²+x√7)⁷ ) ' =7*(x²+x√7)⁶ *(x²+x√7) ' =7*(x²+x√7)⁶ *(2x+√7).