What is the derivative of 4/3 pi(3+x)^3 ?

The derivative of 4/3 pi(3+x)^3 is 4pi(3+x)^2

What is the first derivative of 4/3 pi(3+x)^3 ?

The first derivative of 4/3 pi(3+x)^3 is 4pi(3+x)^2

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derivative of

\frac{4}{3} π (3 + x)^{3}

4 π (3 + x)^{2}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 + x) = 1

= \frac{4}{3} π 3 (3 + x)^{2} \cdot 1

Simplify

\frac{4}{3} π 3 (3 + x)^{2} \cdot 1 : 4 π (3 + x)^{2}

= 4 π (3 + x)^{2}

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What is the derivative of 4/3 pi(3+x)^3 ?
The derivative of 4/3 pi(3+x)^3 is 4pi(3+x)^2
What is the first derivative of 4/3 pi(3+x)^3 ?
The first derivative of 4/3 pi(3+x)^3 is 4pi(3+x)^2