What is the derivative of xy^2-y^3 ?

The derivative of xy^2-y^3 is y^2+2xy(dy)/(dx)-3y^2(dy)/(dx)

What is the first derivative of xy^2-y^3 ?

The first derivative of xy^2-y^3 is y^2+2xy(dy)/(dx)-3y^2(dy)/(dx)

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

n = 1 \sum \infty \frac{sin ( \frac{1}{n} )}{n}

n = 1 \sum \infty 4^{n + 1}

n = 1 \sum \infty \frac{1}{n ^{2} + 6 n}

\int x^{9} e^{x} d x

y^{^{''}} + 4 \cdot y = 3 \cdot x - 1

What is the derivative of xy^2-y^3 ?
The derivative of xy^2-y^3 is y^2+2xy(dy)/(dx)-3y^2(dy)/(dx)
What is the first derivative of xy^2-y^3 ?
The first derivative of xy^2-y^3 is y^2+2xy(dy)/(dx)-3y^2(dy)/(dx)