What is the derivative of sqrt(35x)ln(13x) ?

The derivative of sqrt(35x)ln(13x) is (sqrt(35)ln(13x)}{2sqrt(x)}+sqrt(\frac{35)/x)

What is the first derivative of sqrt(35x)ln(13x) ?

The first derivative of sqrt(35x)ln(13x) is (sqrt(35)ln(13x)}{2sqrt(x)}+sqrt(\frac{35)/x)

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\frac{d}{d x} (35 x ln (13 x))

\frac{35 ln ( 13 x )}{2 x} + \frac{35}{x}

Solution steps

\frac{d}{d x} (35 x ln (13 x))

Apply the Product Rule:

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

f = 35 x, g = ln (13 x)

= \frac{d}{d x} (35 x) ln (13 x) + \frac{d}{d x} (ln (13 x)) 35 x

\frac{d}{d x} (35 x) = \frac{35}{2 x}

\frac{d}{d x} (ln (13 x)) = \frac{1}{x}

= \frac{35}{2 x} ln (13 x) + \frac{1}{x} 35 x

Simplify

\frac{35}{2 x} ln (13 x) + \frac{1}{x} 35 x : \frac{35 ln ( 13 x )}{2 x} + \frac{35}{x}

= \frac{35 ln ( 13 x )}{2 x} + \frac{35}{x}

What is the derivative of sqrt(35x)ln(13x) ?
The derivative of sqrt(35x)ln(13x) is (sqrt(35)ln(13x)}{2sqrt(x)}+sqrt(\frac{35)/x)
What is the first derivative of sqrt(35x)ln(13x) ?
The first derivative of sqrt(35x)ln(13x) is (sqrt(35)ln(13x)}{2sqrt(x)}+sqrt(\frac{35)/x)