What is the derivative of-(5e^{5/x})/(x^2) ?

The derivative of-(5e^{5/x})/(x^2) is -(5(-5e^{5/x}-2e^{5/x}x))/(x^4)

What is the first derivative of-(5e^{5/x})/(x^2) ?

The first derivative of-(5e^{5/x})/(x^2) is -(5(-5e^{5/x}-2e^{5/x}x))/(x^4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

- \frac{5 e ^{\frac{5}{x}}}{x ^{2}}

- \frac{5 ( - 5 e ^{\frac{5}{x}} - 2 e ^{\frac{5}{x}} x )}{x ^{4}}

Solution steps

\frac{d}{d x} (- \frac{5 e ^{\frac{5}{x}}}{x ^{2}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - 5 \frac{d}{d x} (\frac{e ^{\frac{5}{x}}}{x ^{2}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= - 5 \cdot \frac{\frac{d}{d x} ( e ^{\frac{5}{x}} ) x ^{2} - \frac{d}{d x} ( x ^{2} ) e ^{\frac{5}{x}}}{( x ^{2} ) ^{2}}

\frac{d}{d x} (e^{\frac{5}{x}}) = - \frac{5 e ^{\frac{5}{x}}}{x ^{2}}

\frac{d}{d x} (x^{2}) = 2 x

= - 5 \cdot \frac{( - \frac{5 e ^{\frac{5}{x}}}{x ^{2}} ) x ^{2} - 2 x e ^{\frac{5}{x}}}{( x ^{2} ) ^{2}}

Simplify

- 5 \cdot \frac{( - \frac{5 e ^{\frac{5}{x}}}{x ^{2}} ) x ^{2} - 2 x e ^{\frac{5}{x}}}{( x ^{2} ) ^{2}} : - \frac{5 ( - 5 e ^{\frac{5}{x}} - 2 e ^{\frac{5}{x}} x )}{x ^{4}}

= - \frac{5 ( - 5 e ^{\frac{5}{x}} - 2 e ^{\frac{5}{x}} x )}{x ^{4}}

What is the derivative of-(5e^{5/x})/(x^2) ?
The derivative of-(5e^{5/x})/(x^2) is -(5(-5e^{5/x}-2e^{5/x}x))/(x^4)
What is the first derivative of-(5e^{5/x})/(x^2) ?
The first derivative of-(5e^{5/x})/(x^2) is -(5(-5e^{5/x}-2e^{5/x}x))/(x^4)