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Popular >

derivative of (x^2+2xln(2x))

Solution

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

Solution

ln (2 x) (2 x + 2) + x + 2

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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

= ln (2 x) (2 x + 2) + x + 2

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (x^2+2xln(2x)) ?
The derivative of (x^2+2xln(2x)) is ln(2x)(2x+2)+x+2
What is the first derivative of (x^2+2xln(2x)) ?
The first derivative of (x^2+2xln(2x)) is ln(2x)(2x+2)+x+2