What is (\partial)/(\partial x)(e^{4xe^y}) ?

The answer to (\partial)/(\partial x)(e^{4xe^y}) is 4e^{4e^yx+y}

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(\partial)/(\partial x)(e^{4xe^y})

\frac{\partial}{\partial x} (e^{4 x e^{y}})

4 e^{4 e^{y} x + y}

Solution steps

\frac{\partial}{\partial x} (e^{4 x e^{y}})

Treat

y

as a constant

Apply the chain rule:

e^{4 x e^{y}} \frac{\partial}{\partial x} (4 x e^{y})

= e^{4 x e^{y}} \frac{\partial}{\partial x} (4 x e^{y})

\frac{\partial}{\partial x} (4 x e^{y}) = 4 e^{y}

= e^{4 x e^{y}} \cdot 4 e^{y}

Apply exponent rule:

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

e^{4 x e^{y}} e^{y} = e^{4 e^{y} x + y}

= 4 e^{4 e^{y} x + y}

x \to 1 - lim (\frac{2}{x} - \frac{1}{ln ( x )})

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

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

x^{^{''}} + x^{^{'}} - 2 x = 0

y^{^{'}} = - \frac{y}{x}

What is (\partial)/(\partial x)(e^{4xe^y}) ?
The answer to (\partial)/(\partial x)(e^{4xe^y}) is 4e^{4e^yx+y}