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

The answer to (\partial)/(\partial x)(e^{6xe^y}) is 6e^{6e^yx+y}

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

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

6 e^{6 e^{y} x + y}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= e^{6 x e^{y}} \cdot 6 e^{y}

Apply exponent rule:

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

e^{6 x e^{y}} e^{y} = e^{6 e^{y} x + y}

= 6 e^{6 e^{y} x + y}

\frac{d y}{d t} = - 2 t y^{2}

\int_{0}^{2} x^{2} e^{x^{3} + 0} d x

\frac{d}{d x} (\frac{3 x}{4})

\frac{7}{3 x ^{2}}

\frac{\partial}{\partial x} (sin^{3} (2 x))

What is (\partial)/(\partial x)(e^{6xe^y}) ?
The answer to (\partial)/(\partial x)(e^{6xe^y}) is 6e^{6e^yx+y}