What is the derivative of (2x^3+5)^4 ?

The derivative of (2x^3+5)^4 is 24x^2(2x^3+5)^3

What is the first derivative of (2x^3+5)^4 ?

The first derivative of (2x^3+5)^4 is 24x^2(2x^3+5)^3

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derivative of

(2 x^{3} + 5)^{4}

24 x^{2} (2 x^{3} + 5)^{3}

Solution steps

\frac{d}{d x} ((2 x^{3} + 5)^{4})

Apply the chain rule:

4 (2 x^{3} + 5)^{3} \frac{d}{d x} (2 x^{3} + 5)

= 4 (2 x^{3} + 5)^{3} \frac{d}{d x} (2 x^{3} + 5)

\frac{d}{d x} (2 x^{3} + 5) = 6 x^{2}

= 4 (2 x^{3} + 5)^{3} \cdot 6 x^{2}

Simplify

= 24 x^{2} (2 x^{3} + 5)^{3}

What is the derivative of (2x^3+5)^4 ?
The derivative of (2x^3+5)^4 is 24x^2(2x^3+5)^3
What is the first derivative of (2x^3+5)^4 ?
The first derivative of (2x^3+5)^4 is 24x^2(2x^3+5)^3