What is the derivative of (y^2/x) ?

The derivative of (y^2/x) is (2xy\frac{dy)/(dx)-y^2}{x^2}

What is the first derivative of (y^2/x) ?

The first derivative of (y^2/x) is (2xy\frac{dy)/(dx)-y^2}{x^2}

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d x}{d x} = 1

= \frac{2 y \frac{d y}{d x} x - 1 \cdot y ^{2}}{x ^{2}}

Simplify

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

What is the derivative of (y^2/x) ?
The derivative of (y^2/x) is (2xy\frac{dy)/(dx)-y^2}{x^2}
What is the first derivative of (y^2/x) ?
The first derivative of (y^2/x) is (2xy\frac{dy)/(dx)-y^2}{x^2}