What is the derivative of sqrt(15x)ln(4x) ?

The derivative of sqrt(15x)ln(4x) is (sqrt(15)ln(4x)}{2sqrt(x)}+sqrt(\frac{15)/x)

What is the first derivative of sqrt(15x)ln(4x) ?

The first derivative of sqrt(15x)ln(4x) is (sqrt(15)ln(4x)}{2sqrt(x)}+sqrt(\frac{15)/x)

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derivative of

15 x ln (4 x)

\frac{15 ln ( 4 x )}{2 x} + \frac{15}{x}

Solution steps

\frac{d}{d x} (15 x ln (4 x))

Apply the Product Rule:

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

f = 15 x, g = ln (4 x)

= \frac{d}{d x} (15 x) ln (4 x) + \frac{d}{d x} (ln (4 x)) 15 x

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

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

= \frac{15}{2 x} ln (4 x) + \frac{1}{x} 15 x

Simplify

\frac{15}{2 x} ln (4 x) + \frac{1}{x} 15 x : \frac{15 ln ( 4 x )}{2 x} + \frac{15}{x}

= \frac{15 ln ( 4 x )}{2 x} + \frac{15}{x}

\int \frac{8}{5 ^{3 x}} d x

\int \frac{x ^{2} + 12 x + 12}{x ( x ^{2} - 4 )} d x

\frac{d}{d x} (\frac{8 x ^{2} + 6 x + 6}{x})

\int 16 sin^{2} (x co) s^{2} x d x

y^{^{''}} + 4 y = sec^{2} (2 x)

What is the derivative of sqrt(15x)ln(4x) ?
The derivative of sqrt(15x)ln(4x) is (sqrt(15)ln(4x)}{2sqrt(x)}+sqrt(\frac{15)/x)
What is the first derivative of sqrt(15x)ln(4x) ?
The first derivative of sqrt(15x)ln(4x) is (sqrt(15)ln(4x)}{2sqrt(x)}+sqrt(\frac{15)/x)