What is the derivative of-(2e^x/(x^3)+(e^x)/(x^2)) ?

The derivative of-(2e^x/(x^3)+(e^x)/(x^2)) is (e^xx^2-4e^xx+6e^x)/(x^4)

What is the first derivative of-(2e^x/(x^3)+(e^x)/(x^2)) ?

The first derivative of-(2e^x/(x^3)+(e^x)/(x^2)) is (e^xx^2-4e^xx+6e^x)/(x^4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (- \frac{2 e ^{x}}{x ^{3}} + \frac{e ^{x}}{x ^{2}})

\frac{e ^{x} x ^{2} - 4 e ^{x} x + 6 e ^{x}}{x ^{4}}

Solution steps

\frac{d}{d x} (- \frac{2 e ^{x}}{x ^{3}} + \frac{e ^{x}}{x ^{2}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - \frac{d}{d x} (\frac{2 e ^{x}}{x ^{3}}) + \frac{d}{d x} (\frac{e ^{x}}{x ^{2}})

\frac{d}{d x} (\frac{2 e ^{x}}{x ^{3}}) = \frac{2 e ^{x} ( x - 3 )}{x ^{4}}

\frac{d}{d x} (\frac{e ^{x}}{x ^{2}}) = \frac{e ^{x} ( x - 2 )}{x ^{3}}

= - \frac{2 e ^{x} ( x - 3 )}{x ^{4}} + \frac{e ^{x} ( x - 2 )}{x ^{3}}

Simplify

- \frac{2 e ^{x} ( x - 3 )}{x ^{4}} + \frac{e ^{x} ( x - 2 )}{x ^{3}} : \frac{e ^{x} x ^{2} - 4 e ^{x} x + 6 e ^{x}}{x ^{4}}

= \frac{e ^{x} x ^{2} - 4 e ^{x} x + 6 e ^{x}}{x ^{4}}

What is the derivative of-(2e^x/(x^3)+(e^x)/(x^2)) ?
The derivative of-(2e^x/(x^3)+(e^x)/(x^2)) is (e^xx^2-4e^xx+6e^x)/(x^4)
What is the first derivative of-(2e^x/(x^3)+(e^x)/(x^2)) ?
The first derivative of-(2e^x/(x^3)+(e^x)/(x^2)) is (e^xx^2-4e^xx+6e^x)/(x^4)