What is the derivative of x^2log_{e}(2x) ?

The derivative of x^2log_{e}(2x) is 2xln(2x)+x

What is the first derivative of x^2log_{e}(2x) ?

The first derivative of x^2log_{e}(2x) is 2xln(2x)+x

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\frac{d}{d x} (x^{2} lo g_{e} (2 x))

2 x ln (2 x) + x

Solution steps

\frac{d}{d x} (x^{2} lo g_{e} (2 x))

Simplify

x^{2} lo g_{e} (2 x) : x^{2} ln (2 x)

= \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

What is the derivative of x^2log_{e}(2x) ?
The derivative of x^2log_{e}(2x) is 2xln(2x)+x
What is the first derivative of x^2log_{e}(2x) ?
The first derivative of x^2log_{e}(2x) is 2xln(2x)+x