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

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

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

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

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derivative

\frac{4}{2 x - 3}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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