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

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

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

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

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derivative of

x^{2} ln (2 x)

2 x ln (2 x) + x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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

= 2 x ln (2 x) + x

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

\int (3 x^{3} + 4 x^{2} - 2 x^{- 1} + 13) d x

t^{2} cos (5 t)

\frac{sin ( x )}{2 + cos ( x )}

sin (5 x), x = 0

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