What is the derivative of ln((4x^2/(x-6))) ?

The derivative of ln((4x^2/(x-6))) is (x-12)/(x(x-6))

What is the first derivative of ln((4x^2/(x-6))) ?

The first derivative of ln((4x^2/(x-6))) is (x-12)/(x(x-6))

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\frac{d}{d x} (ln (\frac{4 x ^{2}}{x - 6}))

\frac{x - 12}{x ( x - 6 )}

Solution steps

\frac{d}{d x} (ln (\frac{4 x ^{2}}{x - 6}))

Apply the chain rule:

\frac{1}{\frac{4 x ^{2}}{x - 6}} \frac{d}{d x} (\frac{4 x ^{2}}{x - 6})

= \frac{1}{\frac{4 x ^{2}}{x - 6}} \frac{d}{d x} (\frac{4 x ^{2}}{x - 6})

\frac{d}{d x} (\frac{4 x ^{2}}{x - 6}) = \frac{4 ( x ^{2} - 12 x )}{( x - 6 ) ^{2}}

= \frac{1}{\frac{4 x ^{2}}{x - 6}} \cdot \frac{4 ( x ^{2} - 12 x )}{( x - 6 ) ^{2}}

Simplify

\frac{1}{\frac{4 x ^{2}}{x - 6}} \cdot \frac{4 ( x ^{2} - 12 x )}{( x - 6 ) ^{2}} : \frac{x - 12}{x ( x - 6 )}

= \frac{x - 12}{x ( x - 6 )}

\int e^{u} sin (u) d u

\frac{s + 2}{s ^{2} + s}

\int sin^{7} (2 x) cos (2 x) d x

\int \frac{1}{x ^{2} - 2 x + 3} d x

\frac{d y}{d x} = 3 y + a

What is the derivative of ln((4x^2/(x-6))) ?
The derivative of ln((4x^2/(x-6))) is (x-12)/(x(x-6))
What is the first derivative of ln((4x^2/(x-6))) ?
The first derivative of ln((4x^2/(x-6))) is (x-12)/(x(x-6))