What is the derivative of ln(4x-x^2-3) ?

The derivative of ln(4x-x^2-3) is (-2x+4)/(4x-x^2-3)

What is the first derivative of ln(4x-x^2-3) ?

The first derivative of ln(4x-x^2-3) is (-2x+4)/(4x-x^2-3)

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derivative of

ln (4 x - x^{2} - 3)

\frac{- 2 x + 4}{4 x - x ^{2} - 3}

Solution steps

\frac{d}{d x} (ln (4 x - x^{2} - 3))

Apply the chain rule:

\frac{1}{4 x - x ^{2} - 3} \frac{d}{d x} (4 x - x^{2} - 3)

= \frac{1}{4 x - x ^{2} - 3} \frac{d}{d x} (4 x - x^{2} - 3)

\frac{d}{d x} (4 x - x^{2} - 3) = - 2 x + 4

= \frac{1}{4 x - x ^{2} - 3} (- 2 x + 4)

Simplify

\frac{1}{4 x - x ^{2} - 3} (- 2 x + 4) : \frac{- 2 x + 4}{4 x - x ^{2} - 3}

= \frac{- 2 x + 4}{4 x - x ^{2} - 3}

What is the derivative of ln(4x-x^2-3) ?
The derivative of ln(4x-x^2-3) is (-2x+4)/(4x-x^2-3)
What is the first derivative of ln(4x-x^2-3) ?
The first derivative of ln(4x-x^2-3) is (-2x+4)/(4x-x^2-3)