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

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

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

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

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derivative of

y = 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{1 - x}{x} d x

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

\frac{d}{d x} (2 x - y)

\int x^{2} - y^{2} d x

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

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