What is the derivative of-(6e^{6/x}/(x^2)) ?

The derivative of-(6e^{6/x}/(x^2)) is -(6(-6e^{6/x}-2e^{6/x}x))/(x^4)

What is the first derivative of-(6e^{6/x}/(x^2)) ?

The first derivative of-(6e^{6/x}/(x^2)) is -(6(-6e^{6/x}-2e^{6/x}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{6 e ^{\frac{6}{x}}}{x ^{2}})

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

Solution steps

\frac{d}{d x} (- \frac{6 e ^{\frac{6}{x}}}{x ^{2}})

Take the constant out:

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

= - 6 \frac{d}{d x} (\frac{e ^{\frac{6}{x}}}{x ^{2}})

Apply the Quotient Rule:

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

= - 6 \cdot \frac{\frac{d}{d x} ( e ^{\frac{6}{x}} ) x ^{2} - \frac{d}{d x} ( x ^{2} ) e ^{\frac{6}{x}}}{( x ^{2} ) ^{2}}

\frac{d}{d x} (e^{\frac{6}{x}}) = - \frac{6 e ^{\frac{6}{x}}}{x ^{2}}

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

= - 6 \cdot \frac{( - \frac{6 e ^{\frac{6}{x}}}{x ^{2}} ) x ^{2} - 2 x e ^{\frac{6}{x}}}{( x ^{2} ) ^{2}}

Simplify

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

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

What is the derivative of-(6e^{6/x}/(x^2)) ?
The derivative of-(6e^{6/x}/(x^2)) is -(6(-6e^{6/x}-2e^{6/x}x))/(x^4)
What is the first derivative of-(6e^{6/x}/(x^2)) ?
The first derivative of-(6e^{6/x}/(x^2)) is -(6(-6e^{6/x}-2e^{6/x}x))/(x^4)