What is the derivative of (9x^4+5^3) ?

The derivative of (9x^4+5^3) is 108x^3(9x^4+5)^2

What is the first derivative of (9x^4+5^3) ?

The first derivative of (9x^4+5^3) is 108x^3(9x^4+5)^2

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\frac{d}{d x} ((9 x^{4} + 5)^{3})

108 x^{3} (9 x^{4} + 5)^{2}

Solution steps

\frac{d}{d x} ((9 x^{4} + 5)^{3})

Apply the chain rule:

3 (9 x^{4} + 5)^{2} \frac{d}{d x} (9 x^{4} + 5)

= 3 (9 x^{4} + 5)^{2} \frac{d}{d x} (9 x^{4} + 5)

\frac{d}{d x} (9 x^{4} + 5) = 36 x^{3}

= 3 (9 x^{4} + 5)^{2} \cdot 36 x^{3}

Simplify

= 108 x^{3} (9 x^{4} + 5)^{2}

What is the derivative of (9x^4+5^3) ?
The derivative of (9x^4+5^3) is 108x^3(9x^4+5)^2
What is the first derivative of (9x^4+5^3) ?
The first derivative of (9x^4+5^3) is 108x^3(9x^4+5)^2