What is (\partial)/(\partial x)(Ae^{1/x}) ?

The answer to (\partial)/(\partial x)(Ae^{1/x}) is -(Ae^{1/x})/(x^2)

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(\partial)/(\partial x)(Ae^{1/x})

\frac{\partial}{\partial x} (A e^{\frac{1}{x}})

- \frac{A e ^{\frac{1}{x}}}{x ^{2}}

Solution steps

\frac{\partial}{\partial x} (A e^{\frac{1}{x}})

Take the constant out:

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

= A \frac{\partial}{\partial x} (e^{\frac{1}{x}})

Apply the chain rule:

e^{\frac{1}{x}} \frac{\partial}{\partial x} (\frac{1}{x})

= e^{\frac{1}{x}} \frac{\partial}{\partial x} (\frac{1}{x})

\frac{\partial}{\partial x} (\frac{1}{x}) = - \frac{1}{x ^{2}}

= A e^{\frac{1}{x}} (- \frac{1}{x ^{2}})

Simplify

A e^{\frac{1}{x}} (- \frac{1}{x ^{2}}) : - \frac{A e ^{\frac{1}{x}}}{x ^{2}}

= - \frac{A e ^{\frac{1}{x}}}{x ^{2}}

\int_{0}^{6} 2 π (y + 2) (3 - \frac{y}{2}) d y

\frac{d y}{d x} - \frac{y}{x} = 3 x e^{x}

\frac{d}{d x} (ln (x e^{- 5 x}))

\int_{- 2}^{2} (\frac{1}{( x + 4 ) ( x - 4 )}) d x

x \to 0 - lim (csc (x) (x - 1))

What is (\partial)/(\partial x)(Ae^{1/x}) ?
The answer to (\partial)/(\partial x)(Ae^{1/x}) is -(Ae^{1/x})/(x^2)