What is (\partial)/(\partial x)((e^x+e^y)^5) ?

The answer to (\partial)/(\partial x)((e^x+e^y)^5) is 5(e^x+e^y)^4e^x

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(\partial)/(\partial x)((e^x+e^y)^5)

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

= 5 (e^{x} + e^{y})^{4} \frac{\partial}{\partial x} (e^{x} + e^{y})

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

= 5 (e^{x} + e^{y})^{4} e^{x}

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

y^{^{'}} = 3 cos (t) - 2 y

\frac{3}{x + 2}

\int_{1}^{3} (4 x^{3} - 3 x^{2}) d x

\frac{1}{s ^{2} + s}

What is (\partial)/(\partial x)((e^x+e^y)^5) ?
The answer to (\partial)/(\partial x)((e^x+e^y)^5) is 5(e^x+e^y)^4e^x