What is the derivative of (4x-5ln(2x-3)) ?

The derivative of (4x-5ln(2x-3)) is 4ln(2x-3)+(2(4x-5))/(2x-3)

What is the first derivative of (4x-5ln(2x-3)) ?

The first derivative of (4x-5ln(2x-3)) is 4ln(2x-3)+(2(4x-5))/(2x-3)

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\frac{d}{d x} ((4 x - 5) ln (2 x - 3))

4 ln (2 x - 3) + \frac{2 ( 4 x - 5 )}{2 x - 3}

Solution steps

\frac{d}{d x} ((4 x - 5) ln (2 x - 3))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 4 x - 5, g = ln (2 x - 3)

= \frac{d}{d x} (4 x - 5) ln (2 x - 3) + \frac{d}{d x} (ln (2 x - 3)) (4 x - 5)

\frac{d}{d x} (4 x - 5) = 4

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

= 4 ln (2 x - 3) + \frac{2}{2 x - 3} (4 x - 5)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= 4 ln (2 x - 3) + \frac{2 ( 4 x - 5 )}{2 x - 3}

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

\frac{d}{d x} (3 sin (x) - 3 x cos (x))

\frac{d}{d x} (cos^{x} (x))

\int 5 x + \frac{1}{2 x} d x

y = sin (x^{4})

What is the derivative of (4x-5ln(2x-3)) ?
The derivative of (4x-5ln(2x-3)) is 4ln(2x-3)+(2(4x-5))/(2x-3)
What is the first derivative of (4x-5ln(2x-3)) ?
The first derivative of (4x-5ln(2x-3)) is 4ln(2x-3)+(2(4x-5))/(2x-3)