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Popular >

derivative of 3x^3y-y^3

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Popular Examples

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\int ln (x) d x

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\int 7 x^{2} + 5 x - 5 d x

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

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

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\int c x^{2} d x

(\partial)/(\partial u(v))((e^v)/(u(v)+v^2))

\frac{\partial}{\partial u ( v )} (\frac{e ^{v}}{u ( v ) + v ^{2}})

Frequently Asked Questions (FAQ)

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