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

The derivative of (x^2/(y^3)) is (x(-3x\frac{dy)/(dx)+2y)}{y^4}

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

The first derivative of (x^2/(y^3)) is (x(-3x\frac{dy)/(dx)+2y)}{y^4}

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{2 x y ^{3} - 3 y ^{2} \frac{d y}{d x} x ^{2}}{( y ^{3} ) ^{2}} : \frac{x ( - 3 x \frac{d y}{d x} + 2 y )}{y ^{4}}

= \frac{x ( - 3 x \frac{d y}{d x} + 2 y )}{y ^{4}}

x \to 2 lim (x^{2} + x + 2)

x \to 1 lim (sin (x))

r \to 9 lim (\frac{4 r - 3}{11})

x y^{^{'}} - 2 y = 5 x^{2}

\int \frac{x ^{2}}{x ^{6} + 25} d x

What is the derivative of (x^2/(y^3)) ?
The derivative of (x^2/(y^3)) is (x(-3x\frac{dy)/(dx)+2y)}{y^4}
What is the first derivative of (x^2/(y^3)) ?
The first derivative of (x^2/(y^3)) is (x(-3x\frac{dy)/(dx)+2y)}{y^4}