Question

F(x)=e*1/x
Calculate f'(x) ​

Answer 1

`\huge\boxed{f'(x)=-(e^(1)/(x))/(x^2)}`

Explanation:

`(e^x)'=e^x\\\\\bigg[f\bigg(g(x)\bigg)\bigg]'=f'\bigg(g(x)\bigg)\cdot g'(x)\\\\\left((1)/(x)\right)'=-(1)/(x^2)\\\\====================`

`f(x)=e^(1)/(x)=\left(e^(1)/(x)\right)'\cdot\left((1)/(x)\right)'=e^(1)/(x)\cdot\left(-(1)/(x^2)\right)=-(e^(1)/(x))/(x^2)`