What is the derivative of x^3ln(2x) ?

The derivative of x^3ln(2x) is 3x^2ln(2x)+x^2

What is the first derivative of x^3ln(2x) ?

The first derivative of x^3ln(2x) is 3x^2ln(2x)+x^2

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

3 x^{2} ln (2 x) + x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

\frac{1}{x} x^{3} = x^{2}

= 3 x^{2} ln (2 x) + x^{2}

What is the derivative of x^3ln(2x) ?
The derivative of x^3ln(2x) is 3x^2ln(2x)+x^2
What is the first derivative of x^3ln(2x) ?
The first derivative of x^3ln(2x) is 3x^2ln(2x)+x^2