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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (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}

\frac{\partial}{\partial x} (\frac{x ^{2} - 2 x}{( x - 1 ) ^{2}})

\int e^{- b x} d x

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

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

f (x) = lo g_{10} (1 + x^{2})

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