What is the derivative of (8(3x^4+5)^3) ?

The derivative of (8(3x^4+5)^3) is 7776x^3(648x^4+5)^2

What is the first derivative of (8(3x^4+5)^3) ?

The first derivative of (8(3x^4+5)^3) is 7776x^3(648x^4+5)^2

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\frac{d}{d x} ((8 (3 x)^{4} + 5)^{3})

7776 x^{3} (648 x^{4} + 5)^{2}

Solution steps

\frac{d}{d x} ((8 (3 x)^{4} + 5)^{3})

Simplify

(8 (3 x)^{4} + 5)^{3} : (648 x^{4} + 5)^{3}

= \frac{d}{d x} ((648 x^{4} + 5)^{3})

Apply the chain rule:

3 (648 x^{4} + 5)^{2} \frac{d}{d x} (648 x^{4} + 5)

= 3 (648 x^{4} + 5)^{2} \frac{d}{d x} (648 x^{4} + 5)

\frac{d}{d x} (648 x^{4} + 5) = 2592 x^{3}

= 3 (648 x^{4} + 5)^{2} \cdot 2592 x^{3}

Simplify

= 7776 x^{3} (648 x^{4} + 5)^{2}

What is the derivative of (8(3x^4+5)^3) ?
The derivative of (8(3x^4+5)^3) is 7776x^3(648x^4+5)^2
What is the first derivative of (8(3x^4+5)^3) ?
The first derivative of (8(3x^4+5)^3) is 7776x^3(648x^4+5)^2