Question

Найдите производную функции:
1)f(x)=8x^5 -3x^2 +4
2)f(x)=(3-4x)sqrt x
3)f(x)=x^2 -2/x

Answer 1

Ответ:

$1)\ \ f(x)=8x^5-3x^2+4\\\\f'(x)=40x^4-6x\\\\\\2)\ \ f(x)=(3-4x)\, \sqrt{x}\\\\f'(x)=-3\sqrt{x}+\dfrac{3-4x}{2\sqrt{x}}\\\\\\3)\ \ f(x)=\dfrac{x^2-2}{x}\\\\f'(x)=\dfrac{2x\cdot x-(x^2-2)\cdot 1}{x^2}=\dfrac{x^2+2}{x^2}=1+\dfrac{2}{x^2}$

$\star \ \ f(x)=x^2-\dfrac{2}{x}\ \ ,\ \ f'(x)=2x+\dfrac{2}{x^2}\ \ \star$