What is the derivative of ln(2x)*x^2 ?

The derivative of ln(2x)*x^2 is x+2xln(2x)

What is the first derivative of ln(2x)*x^2 ?

The first derivative of ln(2x)*x^2 is x+2xln(2x)

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derivative of

ln (2 x) \cdot x^{2}

x + 2 x ln (2 x)

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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

= x + 2 x ln (2 x)

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