What is the derivative of (2x^2+9)^3 ?

The derivative of (2x^2+9)^3 is 12x(2x^2+9)^2

What is the first derivative of (2x^2+9)^3 ?

The first derivative of (2x^2+9)^3 is 12x(2x^2+9)^2

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derivative of

(2 x^{2} + 9)^{3}

12 x (2 x^{2} + 9)^{2}

Solution steps

\frac{d}{d x} ((2 x^{2} + 9)^{3})

Apply the chain rule:

3 (2 x^{2} + 9)^{2} \frac{d}{d x} (2 x^{2} + 9)

= 3 (2 x^{2} + 9)^{2} \frac{d}{d x} (2 x^{2} + 9)

\frac{d}{d x} (2 x^{2} + 9) = 4 x

= 3 (2 x^{2} + 9)^{2} \cdot 4 x

Simplify

= 12 x (2 x^{2} + 9)^{2}

What is the derivative of (2x^2+9)^3 ?
The derivative of (2x^2+9)^3 is 12x(2x^2+9)^2
What is the first derivative of (2x^2+9)^3 ?
The first derivative of (2x^2+9)^3 is 12x(2x^2+9)^2