What is (\partial)/(\partial x)(e^{6/x}) ?

The answer to (\partial)/(\partial x)(e^{6/x}) is -(6e^{6/x})/(x^2)

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(\partial)/(\partial x)(e^{6/x})

\frac{\partial}{\partial x} (e^{\frac{6}{x}})

- \frac{6 e ^{\frac{6}{x}}}{x ^{2}}

Solution steps

\frac{\partial}{\partial x} (e^{\frac{6}{x}})

Apply the chain rule:

e^{\frac{6}{x}} \frac{\partial}{\partial x} (\frac{6}{x})

= e^{\frac{6}{x}} \frac{\partial}{\partial x} (\frac{6}{x})

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

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

Simplify

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

= - \frac{6 e ^{\frac{6}{x}}}{x ^{2}}

\frac{d}{d t} (e^{- t} (2 cos (\frac{t}{2}) - 3 sin (\frac{t}{2})))

(x^{2} + 16) \frac{d y}{d x} + x y - 4 x = 0

\frac{7}{4 x ^{5}}

\frac{d x}{d t} = (\frac{6 x}{2000 + 12 t})

\int_{1}^{4} 1 e^{x} d x

What is (\partial)/(\partial x)(e^{6/x}) ?
The answer to (\partial)/(\partial x)(e^{6/x}) is -(6e^{6/x})/(x^2)