What is (\partial)/(\partial x)((e^x+e^y)^7) ?

The answer to (\partial)/(\partial x)((e^x+e^y)^7) is 7(e^x+e^y)^6e^x

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(\partial)/(\partial x)((e^x+e^y)^7)

\frac{\partial}{\partial x} ((e^{x} + e^{y})^{7})

7 (e^{x} + e^{y})^{6} e^{x}

Solution steps

\frac{\partial}{\partial x} ((e^{x} + e^{y})^{7})

Treat

y

as a constant

Apply the chain rule:

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

= 7 (e^{x} + e^{y})^{6} \frac{\partial}{\partial x} (e^{x} + e^{y})

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

= 7 (e^{x} + e^{y})^{6} e^{x}

\frac{\partial}{\partial x} (x ln (z^{3} + x^{3}))

\int 9 1 + e^{x} d x

y^{^{''}} + 2 y^{^{'}} + 2 y = e^{- t}, y (0) = 0, y^{^{'}} (0) = 1

\frac{d}{d x} (x^{2} - 3 x + 5)

\frac{d}{d x} (- \frac{11}{x ^{6}})

What is (\partial)/(\partial x)((e^x+e^y)^7) ?
The answer to (\partial)/(\partial x)((e^x+e^y)^7) is 7(e^x+e^y)^6e^x