What is the derivative of 4/3 pi*x^3 ?

The derivative of 4/3 pi*x^3 is 4pix^2

What is the first derivative of 4/3 pi*x^3 ?

The first derivative of 4/3 pi*x^3 is 4pix^2

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\frac{d}{d x} (\frac{4}{3} π \cdot x^{3})

4 π x^{2}

Solution steps

\frac{d}{d x} (\frac{4}{3} π x^{3})

Take the constant out:

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

= \frac{4}{3} π \frac{d}{d x} (x^{3})

Apply the Power Rule:

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

= \frac{4}{3} π 3 x^{3 - 1}

Simplify

\frac{4}{3} π 3 x^{3 - 1} : 4 π x^{2}

= 4 π x^{2}

What is the derivative of 4/3 pi*x^3 ?
The derivative of 4/3 pi*x^3 is 4pix^2
What is the first derivative of 4/3 pi*x^3 ?
The first derivative of 4/3 pi*x^3 is 4pix^2