Question

Найдите производную.
1) f(x)=x^4-2x^3-7
2)f(x)=1/2x^5+4√x -5x^-4
3)f(x)=(x-1)(x+4)
4)f(x)=3 1/4x^6+2x^-1 - e^4
5)f(x)=x-2/x+7

Answer 1

Ответ:

$1)\ \ f(x)=x^4-2x^3-7\ \ ,\ \ f'(x)=4x^3-6x^2\\\\\\2)\ \ f(x)=\dfrac{1}{2}\, x^5+4\sqrt{x}-5x^{-4}\\\\f'(x)=\dfrac{1}{2}\cdot 5x^4+4\cdot \dfrac{1}{2\sqrt{x}}-5\cdot (-4x^{-5})=\dfrac{5}{2}\, x^4+\dfrac{2}{\sqrt{x}}+\dfrac{20}{x^5}\\\\\\3)\ \ f(x)=(x-1)(x+4)=x^2+3x-4\ \ ,\ \ \ f'(x)=2x+3$

$4)\ \ f(x)=3\dfrac{1}{4}\, x^6+2x^{-1}-e^4\ \ ,\\\\f'(x)=\dfrac{13}{4}\cdot 6x^5-2x^{-2}-0=\dfrac{39}{2}\, x^5-\dfrac{2}{x^2}\\\\\\5)\ \ f(x)=\dfrac{x-2}{x-7}\\\\f'(x)=\dfrac{1\cdot (x-7)-1\cdot (x-2)}{(x-7)^2}=\dfrac{-5}{(x-7)^2}$