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

The derivative of sqrt(x)ln(2x) is (ln(2x))/(2sqrt(x))+1/(sqrt(x))

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

The first derivative of sqrt(x)ln(2x) is (ln(2x))/(2sqrt(x))+1/(sqrt(x))

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

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = ln (2 x)

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

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

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

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

Simplify

\frac{1}{2 x} ln (2 x) + \frac{1}{x} x : \frac{ln ( 2 x )}{2 x} + \frac{1}{x}

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

x \to 2 + lim (x^{2})

b^{x}

\int \frac{2 x}{2 x + 1} d x

x y^{2} + 1 + x^{2} \frac{d y}{d x} = 0

What is the derivative of sqrt(x)ln(2x) ?
The derivative of sqrt(x)ln(2x) is (ln(2x))/(2sqrt(x))+1/(sqrt(x))
What is the first derivative of sqrt(x)ln(2x) ?
The first derivative of sqrt(x)ln(2x) is (ln(2x))/(2sqrt(x))+1/(sqrt(x))