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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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