What is the derivative of (y^3/(x^2)) ?

The derivative of (y^3/(x^2)) is (y^2(3x\frac{dy)/(dx)-2y)}{x^3}

What is the first derivative of (y^3/(x^2)) ?

The first derivative of (y^3/(x^2)) is (y^2(3x\frac{dy)/(dx)-2y)}{x^3}

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\frac{d}{d x} (\frac{y ^{3}}{x ^{2}})

\frac{y ^{2} ( 3 x \frac{d y}{d x} - 2 y )}{x ^{3}}

Solution steps

\frac{d}{d x} (\frac{y ^{3}}{x ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( y ^{3} ) x ^{2} - \frac{d}{d x} ( x ^{2} ) y ^{3}}{( x ^{2} ) ^{2}}

\frac{d}{d x} (y^{3}) = 3 y^{2} \frac{d y}{d x}

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

= \frac{3 y ^{2} \frac{d y}{d x} x ^{2} - 2 x y ^{3}}{( x ^{2} ) ^{2}}

Simplify

\frac{3 y ^{2} \frac{d y}{d x} x ^{2} - 2 x y ^{3}}{( x ^{2} ) ^{2}} : \frac{y ^{2} ( 3 x \frac{d y}{d x} - 2 y )}{x ^{3}}

= \frac{y ^{2} ( 3 x \frac{d y}{d x} - 2 y )}{x ^{3}}

\frac{\partial}{\partial y} (x^{5} y)

\int cos (2 t) e^{- s t} d t

\frac{d}{d x} (\frac{f ( x )}{x ^{4}})

\frac{\partial}{\partial x} (2 x - 3 cos (x) + 10 y)

\frac{d}{d x} (\frac{8}{x} - \frac{2}{x ^{3}} + \frac{1}{x ^{4}})

What is the derivative of (y^3/(x^2)) ?
The derivative of (y^3/(x^2)) is (y^2(3x\frac{dy)/(dx)-2y)}{x^3}
What is the first derivative of (y^3/(x^2)) ?
The first derivative of (y^3/(x^2)) is (y^2(3x\frac{dy)/(dx)-2y)}{x^3}