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

The answer to (\partial)/(\partial x)(e^{xe^x}) is e^{xe^x}(e^x+e^xx)

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

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

e^{x e^{x}} (e^{x} + e^{x} x)

Solution steps

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

Apply the chain rule:

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

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

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

= e^{x e^{x}} (e^{x} + e^{x} x)

\int x tan (x) d x

\int_{1}^{e} 5 x^{2} ln (x) d x

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

\frac{d}{d x} (ln (8 x^{2} + 1))

\int \frac{- 3 x ^{3} + 2 x ^{2} - 3 x - 6}{x ^{3} + x} d x

What is (\partial)/(\partial x)(e^{xe^x}) ?
The answer to (\partial)/(\partial x)(e^{xe^x}) is e^{xe^x}(e^x+e^xx)