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

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

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

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

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derivative of

f (x) = 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}

\frac{d}{d x} (\frac{7 - x e ^{x}}{x + e ^{x}})

\frac{( s - 1 )}{2 s ^{2} + 8 s + 11}

\int \frac{e ^{x - 5} - e ^{3 + x}}{e ^{1 - x}} d x

f (x) = (1 + 8 x^{2}) (x - x^{2})

\frac{d}{d x} (e^{x - 8})

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