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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{x ^{2}}{2 + x} d x

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

\int \frac{a ^{2} - x ^{2}}{x ^{2}} d x

y = 11 x, y = x^{2} - 12

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

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