What is (\partial)/(\partial y)((e^x+e^y)^3) ?

The answer to (\partial)/(\partial y)((e^x+e^y)^3) is 3(e^x+e^y)^2e^y

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(\partial)/(\partial y)((e^x+e^y)^3)

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

3 (e^{x} + e^{y})^{2} e^{y}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

3 (e^{x} + e^{y})^{2} \frac{\partial}{\partial y} (e^{x} + e^{y})

= 3 (e^{x} + e^{y})^{2} \frac{\partial}{\partial y} (e^{x} + e^{y})

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

= 3 (e^{x} + e^{y})^{2} e^{y}

y = 2 tan (cos (3 x)) + \frac{sin ( x ^{3} )}{x ^{2}}

x \to 7 - lim (\frac{x + 8}{x - 7})

\int 4 sin (3 x) d x

\int_{0}^{0.5} 200 x d x

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

What is (\partial)/(\partial y)((e^x+e^y)^3) ?
The answer to (\partial)/(\partial y)((e^x+e^y)^3) is 3(e^x+e^y)^2e^y