What is (\partial)/(\partial x)(e^{5xe^y}) ?

The answer to (\partial)/(\partial x)(e^{5xe^y}) is 5e^{5e^yx+y}

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(\partial)/(\partial x)(e^{5xe^y})

\frac{\partial}{\partial x} (e^{5 x e^{y}})

5 e^{5 e^{y} x + y}

Solution steps

\frac{\partial}{\partial x} (e^{5 x e^{y}})

Treat

y

as a constant

Apply the chain rule:

e^{5 x e^{y}} \frac{\partial}{\partial x} (5 x e^{y})

= e^{5 x e^{y}} \frac{\partial}{\partial x} (5 x e^{y})

\frac{\partial}{\partial x} (5 x e^{y}) = 5 e^{y}

= e^{5 x e^{y}} \cdot 5 e^{y}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{5 x e^{y}} e^{y} = e^{5 e^{y} x + y}

= 5 e^{5 e^{y} x + y}

\int_{- 1}^{1} (2 x + 3) d x

\int x^{a} ln (x) d x

\int e^{12 x} d x

π t

\frac{d}{d x} (\frac{125}{x})

What is (\partial)/(\partial x)(e^{5xe^y}) ?
The answer to (\partial)/(\partial x)(e^{5xe^y}) is 5e^{5e^yx+y}