What is (\partial)/(\partial x)(e^{9xe^y}) ?

The answer to (\partial)/(\partial x)(e^{9xe^y}) is 9e^{9e^yx+y}

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(\partial)/(\partial x)(e^{9xe^y})

\frac{\partial}{\partial x} (e^{9 x e^{y}})

9 e^{9 e^{y} x + y}

Solution steps

\frac{\partial}{\partial x} (e^{9 x e^{y}})

Treat

y

as a constant

Apply the chain rule:

e^{9 x e^{y}} \frac{\partial}{\partial x} (9 x e^{y})

= e^{9 x e^{y}} \frac{\partial}{\partial x} (9 x e^{y})

\frac{\partial}{\partial x} (9 x e^{y}) = 9 e^{y}

= e^{9 x e^{y}} \cdot 9 e^{y}

Apply exponent rule:

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

e^{9 x e^{y}} e^{y} = e^{9 e^{y} x + y}

= 9 e^{9 e^{y} x + y}

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

\int csc^{9} (x) d x

x \to 0 lim (x^{2} - 3 x + 3)

\frac{d}{d x} (\frac{2 x}{x})

x \to 0 + lim (\frac{3}{x})

What is (\partial)/(\partial x)(e^{9xe^y}) ?
The answer to (\partial)/(\partial x)(e^{9xe^y}) is 9e^{9e^yx+y}