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)

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derivative of

- \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}}

\frac{d}{d x} (\frac{5 x ^{2}}{2 b ^{2} + x ^{2}})

(y^{2} + x y) d x + x^{2} d y = 0

20 y^{^{''}} + 11 y^{^{'}} - 3 y = 0

\frac{d}{d y} (\frac{z}{( x ^{2} + y ^{2} + z ^{2} ) ^{\frac{3}{2}}})

x \to 1 lim (\frac{x ^{2} - 3 x + 2}{x ^{3} - 1})

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)