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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

f (x) = 2 tan (x)

\int - \frac{3 sin ( - x )}{cos ( - x )} d x

\int_{- 1}^{1} π (8 - 8 x^{2})^{2} d x

f (x) = x - (x + 1)^{4}

y^{^{'}} = x - 7

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