What is the derivative of 1/(xe^x) ?

The derivative of 1/(xe^x) is -(1+x)/(e^xx^2)

What is the first derivative of 1/(xe^x) ?

The first derivative of 1/(xe^x) is -(1+x)/(e^xx^2)

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

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

\frac{d}{d x} (x e^{x}) = e^{x} + e^{x} x

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

Simplify

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

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

\frac{\partial}{\partial s} (3 s + t)

f (x) = 3 csc (x) - 5 sec (x)

\int \frac{x + 2}{x ^{2} + 4 x + 1} d x

\int (sinh (x) - cosh (x)) e^{- x} d x

x^{2} d x - y (1 + x^{3}) d y = 0

What is the derivative of 1/(xe^x) ?
The derivative of 1/(xe^x) is -(1+x)/(e^xx^2)
What is the first derivative of 1/(xe^x) ?
The first derivative of 1/(xe^x) is -(1+x)/(e^xx^2)