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Popular >

derivative of (x-2^3e^{3x})

Solution

\frac{d}{d x} ((x - 2)^{3} e^{3 x})

Solution

3 (x - 2)^{2} e^{3 x} + e^{3 x} \cdot 3 (x - 2)^{3}

Solution steps

\frac{d}{d x} ((x - 2)^{3} e^{3 x})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = (x - 2)^{3}, g = e^{3 x}

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

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

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

= 3 (x - 2)^{2} e^{3 x} + e^{3 x} \cdot 3 (x - 2)^{3}

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Frequently Asked Questions (FAQ)

What is the derivative of (x-2^3e^{3x}) ?
The derivative of (x-2^3e^{3x}) is 3(x-2)^2e^{3x}+e^{3x}*3(x-2)^3
What is the first derivative of (x-2^3e^{3x}) ?
The first derivative of (x-2^3e^{3x}) is 3(x-2)^2e^{3x}+e^{3x}*3(x-2)^3