What is (\partial)/(\partial x)((e^x+e^y)^6) ?

The answer to (\partial)/(\partial x)((e^x+e^y)^6) is 6(e^x+e^y)^5e^x

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(\partial)/(\partial x)((e^x+e^y)^6)

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

= 6 (e^{x} + e^{y})^{5} \frac{\partial}{\partial x} (e^{x} + e^{y})

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

= 6 (e^{x} + e^{y})^{5} e^{x}

\int \frac{1 - x ^{2}}{( x ^{2} - 1 ) ^{2}} d x

x \to 2 lim (x^{2} - 3 x)

y^{^{''}} + 2 y^{^{'}} = 2 x + 7 - e - 2 x

\int sin (2 x) cos^{4} (2 x) d x

f (x) = (7 x + 6)^{2}

What is (\partial)/(\partial x)((e^x+e^y)^6) ?
The answer to (\partial)/(\partial x)((e^x+e^y)^6) is 6(e^x+e^y)^5e^x