What is (\partial)/(\partial x)((e^x+e^y)^4) ?

The answer to (\partial)/(\partial x)((e^x+e^y)^4) is 4(e^x+e^y)^3e^x

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(\partial)/(\partial x)((e^x+e^y)^4)

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

4 (e^{x} + e^{y})^{3} e^{x}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

4 (e^{x} + e^{y})^{3} \frac{\partial}{\partial x} (e^{x} + e^{y})

= 4 (e^{x} + e^{y})^{3} \frac{\partial}{\partial x} (e^{x} + e^{y})

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

= 4 (e^{x} + e^{y})^{3} e^{x}

\frac{d}{d x} (7 x + 9)

f (t) = (1 + t) (2 t^{2} - 7)

\int x^{1} \frac{( 5 x ^{2} + \frac{2}{3} ) ^{4}}{1} d x

\frac{d}{d t} ((\frac{d}{d t} (e^{t} cos (t)))^{2})

f (x) = \frac{e ^{x^{2}}}{x ^{3}}

What is (\partial)/(\partial x)((e^x+e^y)^4) ?
The answer to (\partial)/(\partial x)((e^x+e^y)^4) is 4(e^x+e^y)^3e^x