What is the derivative of (e^{3x}-1)^5 ?

The derivative of (e^{3x}-1)^5 is 15e^{3x}(e^{3x}-1)^4

What is the first derivative of (e^{3x}-1)^5 ?

The first derivative of (e^{3x}-1)^5 is 15e^{3x}(e^{3x}-1)^4

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derivative of

(e^{3 x} - 1)^{5}

15 e^{3 x} (e^{3 x} - 1)^{4}

Solution steps

\frac{d}{d x} ((e^{3 x} - 1)^{5})

Apply the chain rule:

5 (e^{3 x} - 1)^{4} \frac{d}{d x} (e^{3 x} - 1)

= 5 (e^{3 x} - 1)^{4} \frac{d}{d x} (e^{3 x} - 1)

\frac{d}{d x} (e^{3 x} - 1) = 3 e^{3 x}

= 5 (e^{3 x} - 1)^{4} \cdot 3 e^{3 x}

Simplify

= 15 e^{3 x} (e^{3 x} - 1)^{4}

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What is the derivative of (e^{3x}-1)^5 ?
The derivative of (e^{3x}-1)^5 is 15e^{3x}(e^{3x}-1)^4
What is the first derivative of (e^{3x}-1)^5 ?
The first derivative of (e^{3x}-1)^5 is 15e^{3x}(e^{3x}-1)^4