What is the derivative of sqrt(15x)*ln(20x) ?

The derivative of sqrt(15x)*ln(20x) is (sqrt(15)ln(20x)}{2sqrt(x)}+sqrt(\frac{15)/x)

What is the first derivative of sqrt(15x)*ln(20x) ?

The first derivative of sqrt(15x)*ln(20x) is (sqrt(15)ln(20x)}{2sqrt(x)}+sqrt(\frac{15)/x)

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derivative of

15 x \cdot ln (20 x)

\frac{15 ln ( 20 x )}{2 x} + \frac{15}{x}

Solution steps

\frac{d}{d x} (15 x ln (20 x))

Apply the Product Rule:

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

f = 15 x, g = ln (20 x)

= \frac{d}{d x} (15 x) ln (20 x) + \frac{d}{d x} (ln (20 x)) 15 x

\frac{d}{d x} (15 x) = \frac{15}{2 x}

\frac{d}{d x} (ln (20 x)) = \frac{1}{x}

= \frac{15}{2 x} ln (20 x) + \frac{1}{x} 15 x

Simplify

\frac{15}{2 x} ln (20 x) + \frac{1}{x} 15 x : \frac{15 ln ( 20 x )}{2 x} + \frac{15}{x}

= \frac{15 ln ( 20 x )}{2 x} + \frac{15}{x}

x \to 1 lim ((x^{2} - 9)^{\frac{1}{3}})

\frac{d}{d x} (x e^{x^{5}})

\int cos (7 x) cos (9 x) d x

n \to \infty lim (e^{n x})

\int 3 x^{2} sin (\frac{x}{2}) d x

What is the derivative of sqrt(15x)*ln(20x) ?
The derivative of sqrt(15x)*ln(20x) is (sqrt(15)ln(20x)}{2sqrt(x)}+sqrt(\frac{15)/x)
What is the first derivative of sqrt(15x)*ln(20x) ?
The first derivative of sqrt(15x)*ln(20x) is (sqrt(15)ln(20x)}{2sqrt(x)}+sqrt(\frac{15)/x)