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Popular >

derivative of x^3ln(2x)

Solution

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

Solution

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}

Popular Examples

integral of 1/(2-8x)

\int \frac{1}{2 - 8 x} d x

limit as x approaches 2 of-((1/2)/(x-2))

x \to 2 lim (- (\frac{\frac{1}{2}}{x - 2}))

derivative of 1/(16x^2)

\frac{d}{d x} (\frac{1}{16 x ^{2}})

derivative of sqrt(3+6x)

\frac{d}{d x} (3 + 6 x)

integral from 0 to 9 of sqrt(x)-1/3 x

\int_{0}^{9} x - \frac{1}{3} x d x

Frequently Asked Questions (FAQ)

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