What is (\partial)/(\partial x)(2pisqrt(x/y)) ?

The answer to (\partial)/(\partial x)(2pisqrt(x/y)) is pi/(sqrt(x)\sqrt{y)}

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(\partial)/(\partial x)(2pisqrt(x/y))

\frac{\partial}{\partial x} (2 π \frac{x}{y})

\frac{π}{x y}

Solution steps

\frac{\partial}{\partial x} (2 π \frac{x}{y})

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= 2 π \frac{1}{2 \frac{x}{y}} \cdot \frac{1}{y}

Simplify

2 π \frac{1}{2 \frac{x}{y}} \cdot \frac{1}{y} : \frac{π}{x y}

= \frac{π}{x y}

2 y d x = 3 x d y

n = 1 \sum \infty \frac{1}{2 + 3 ^{n}}

t y^{^{'}} + (2 t^{2} + 1) y = 3 t

x, - 1, 2

\int \frac{1}{z ^{3} z ^{2} - 36} d z

What is (\partial)/(\partial x)(2pisqrt(x/y)) ?
The answer to (\partial)/(\partial x)(2pisqrt(x/y)) is pi/(sqrt(x)\sqrt{y)}