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Popular Calculus >

derivative of sqrt(3x)ln(15x)

Solution

derivative of

3 x ln (15 x)

Solution

\frac{3 ln ( 15 x )}{2 x} + \frac{3}{x}

Solution steps

\frac{d}{d x} (3 x ln (15 x))

Apply the Product Rule:

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

f = 3 x, g = ln (15 x)

= \frac{d}{d x} (3 x) ln (15 x) + \frac{d}{d x} (ln (15 x)) 3 x

\frac{d}{d x} (3 x) = \frac{3}{2 x}

\frac{d}{d x} (ln (15 x)) = \frac{1}{x}

= \frac{3}{2 x} ln (15 x) + \frac{1}{x} 3 x

Simplify

\frac{3}{2 x} ln (15 x) + \frac{1}{x} 3 x : \frac{3 ln ( 15 x )}{2 x} + \frac{3}{x}

= \frac{3 ln ( 15 x )}{2 x} + \frac{3}{x}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of sqrt(3x)ln(15x) ?
The derivative of sqrt(3x)ln(15x) is (sqrt(3)ln(15x))/(2sqrt(x))+sqrt(3/x)
What is the first derivative of sqrt(3x)ln(15x) ?
The first derivative of sqrt(3x)ln(15x) is (sqrt(3)ln(15x))/(2sqrt(x))+sqrt(3/x)