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Popular >

derivative of e^{2x}*ln(3x)

Solution

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

Solution

2 e^{2 x} ln (3 x) + \frac{e ^{2 x}}{x}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (e^{2 x}) = e^{2 x} \cdot 2

\frac{d}{d x} (ln (3 x)) = \frac{1}{x}

= e^{2 x} \cdot 2 ln (3 x) + \frac{1}{x} e^{2 x}

\frac{1}{x} e^{2 x} = \frac{e ^{2 x}}{x}

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

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Frequently Asked Questions (FAQ)

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