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Popular >

derivative of ln((4x^2-9/(2x-3)))

Solution

\frac{d}{d x} (ln (\frac{4 x ^{2} - 9}{2 x - 3}))

Solution

\frac{2}{2 x + 3}

Solution steps

\frac{d}{d x} (ln (\frac{4 x ^{2} - 9}{2 x - 3}))

Simplify

ln (\frac{4 x ^{2} - 9}{2 x - 3}) : ln (2 x + 3)

= \frac{d}{d x} (ln (2 x + 3))

Apply the chain rule:

\frac{1}{2 x + 3} \frac{d}{d x} (2 x + 3)

= \frac{1}{2 x + 3} \frac{d}{d x} (2 x + 3)

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

= \frac{1}{2 x + 3} \cdot 2

Simplify

\frac{1}{2 x + 3} \cdot 2 : \frac{2}{2 x + 3}

= \frac{2}{2 x + 3}

Popular Examples

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\frac{\partial}{\partial y} (x^{3} - 3 x y + y^{3})

derivative of x^2sin^3(x)+xcos^{-3}(x)derivative of

x^{2} sin^{3} (x) + x cos^{- 3} (x)

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x \to \infty lim (x^{2} + 6)

tangent of f(x)=(4x+4)^{1/3},\at x=1 tangent of

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Frequently Asked Questions (FAQ)

What is the derivative of ln((4x^2-9/(2x-3))) ?
The derivative of ln((4x^2-9/(2x-3))) is 2/(2x+3)
What is the first derivative of ln((4x^2-9/(2x-3))) ?
The first derivative of ln((4x^2-9/(2x-3))) is 2/(2x+3)