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Popular >

derivative of log_{e}((4x^2-9/(2x-3)))

Solution

\frac{d}{d x} (lo g_{e} (\frac{4 x ^{2} - 9}{2 x - 3}))

Solution

\frac{2}{2 x + 3}

Solution steps

\frac{d}{d x} (lo g_{e} (\frac{4 x ^{2} - 9}{2 x - 3}))

Simplify

lo g_{e} (\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

integral from-infinity to infinity of x^{23}e^{-x^{24}}

\int_{- \infty}^{\infty} x^{23} e^{- x^{24}} d x

(\partial)/(\partial y)(2/(y^2-x))

\frac{\partial}{\partial y} (\frac{2}{y ^{2} - x})

integral of (xe^{2x}+4e^x)/(xe^x)

\int \frac{x e ^{2 x} + 4 e ^{x}}{x e ^{x}} d x

area y=4x+26,(-1,5)area

y = 4 x + 26, (- 1, 5)

derivative of v(t)=t^2e^{-3t}derivative of

v (t) = t^{2} e^{- 3 t}

Frequently Asked Questions (FAQ)

What is the derivative of log_{e}((4x^2-9/(2x-3))) ?
The derivative of log_{e}((4x^2-9/(2x-3))) is 2/(2x+3)
What is the first derivative of log_{e}((4x^2-9/(2x-3))) ?
The first derivative of log_{e}((4x^2-9/(2x-3))) is 2/(2x+3)