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

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

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

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

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

- x^{2}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

= - x^{2}

y^{^{''}} + 4 y^{^{'}} + 4 y = 0, y (0) = 1, y^{^{'}} (0) = 0

\int_{\frac{1}{2}}^{1} (x^{- 3} - 25) d x

y^{^{''}} + \frac{1}{x} y^{^{'}} = 0

y^{^{''}} + 2 x = 6 x^{2}, y (0) = 3

\int_{- 3}^{3} π (9 - x^{2})^{2} d x

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