What is (\partial)/(\partial x)(e^{sqrt(xy)}) ?

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

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(\partial)/(\partial x)(e^{sqrt(xy)})

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{4}{( x + 4 ) ^{2}})

t \cdot \frac{d y}{d t} = t^{3} + 22 t^{3} y

y = \frac{x}{ln ( x )}

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

\int \frac{1}{4 x - x ^{2}} d x

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