What is (\partial)/(\partial x)(e^{2sqrt(x+y)}) ?

The answer to (\partial)/(\partial x)(e^{2sqrt(x+y)}) is (e^{2sqrt(x+y)})/(sqrt(x+y))

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(\partial)/(\partial x)(e^{2sqrt(x+y)})

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

\frac{e ^{2 x + y}}{x + y}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (2 x + y) = \frac{1}{x + y}

= e^{2 x + y} \frac{1}{x + y}

Simplify

e^{2 x + y} \frac{1}{x + y} : \frac{e ^{2 x + y}}{x + y}

= \frac{e ^{2 x + y}}{x + y}

y = - 6 x^{5} + 2

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