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Popular >

derivative of sqrt(x)ln(4x)

Solution

\frac{d}{d x} (x ln (4 x))

Solution

\frac{ln ( 4 x )}{2 x} + \frac{1}{x}

Solution steps

\frac{d}{d x} (x ln (4 x))

Apply the Product Rule:

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

f = x, g = ln (4 x)

= \frac{d}{d x} (x) ln (4 x) + \frac{d}{d x} (ln (4 x)) x

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

\frac{d}{d x} (ln (4 x)) = \frac{1}{x}

= \frac{1}{2 x} ln (4 x) + \frac{1}{x} x

Simplify

\frac{1}{2 x} ln (4 x) + \frac{1}{x} x : \frac{ln ( 4 x )}{2 x} + \frac{1}{x}

= \frac{ln ( 4 x )}{2 x} + \frac{1}{x}

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x \to 1 lim (ln (x) - ln (x - 1))

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x \to 0 lim (\frac{x}{x ^{2} + y ^{2}})

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x)ln(4x) ?
The derivative of sqrt(x)ln(4x) is (ln(4x))/(2sqrt(x))+1/(sqrt(x))
What is the first derivative of sqrt(x)ln(4x) ?
The first derivative of sqrt(x)ln(4x) is (ln(4x))/(2sqrt(x))+1/(sqrt(x))