Question

Найдите производную функции?
1)2x^4-1/x^5
2)(1/7-x/5)^3
3)4^x*cosX
4)sinX-e^x

Answer 1

$f(x)=2x^4-\dfrac{1}{x^5} =2x^4-x^{-5}\\f'(x)=2\cdot4x^3-(-5x^{-6})=8x^3+\dfrac{5}{x^6}$

$f(x)=\left(\dfrac{1}{7}-\dfrac{x}{5}\right)^3\\f'(x)=3\left(\dfrac{1}{7}-\dfrac{x}{5}\right)^2\cdot\left(\dfrac{1}{7}-\dfrac{x}{5}\right)'=3\left(\dfrac{1}{7}-\dfrac{x}{5}\right)^2\cdot\left(-\dfrac{1}{5}\right)=-\dfrac{3}{5}\left(\dfrac{1}{7}-\dfrac{x}{5}\right)^2$

$f(x)=4^x\cdot\cos x\\f'(x)=(4^x)'\cdot\cos x+4^x\cdot(\cos x)'=4^x\cdot\ln4\cdot\cos x+4^x\cdot(-\sin x)=\\=4^x(\ln4\cdot\cos x-\sin x)$

$f(x)=\sin x-e^x\\f'(x)=\cos x-e^x$