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Popular >

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

Solution

derivative of

e^{2 x} ln (2 x)

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (ln (2 x)) = \frac{1}{x}

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

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

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

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Frequently Asked Questions (FAQ)

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