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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int_{1}^{e} 4 x^{2} ln (x) d x

\frac{d}{d x} (\frac{1}{1 + x})

\frac{d}{d x} (e^{\frac{1}{2}})

\int \frac{1 - x}{x ^{3}} d x

\frac{d y}{d x} = (x - 18)^{2}

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