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

The derivative of (-x^3)/(y^3) is -(3x^2)/(y^3)

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

The first derivative of (-x^3)/(y^3) is -(3x^2)/(y^3)

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derivative of

\frac{- x ^{3}}{y ^{3}}

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

Solution steps

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

Simplify

\frac{- x ^{3}}{y ^{3}} : - \frac{x ^{3}}{y ^{3}}

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{1}{y ^{3}} \frac{d}{d x} (x^{3})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= - \frac{1}{y ^{3}} \cdot 3 x^{3 - 1}

Simplify

- \frac{1}{y ^{3}} \cdot 3 x^{3 - 1} : - \frac{3 x ^{2}}{y ^{3}}

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

y = 4 x, y = 2 x^{2}

14 x^{3} + 7 x^{2} + 11 x - 29

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\int \frac{1}{2} e^{5 x + 6} d x

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