What is the derivative of (4x-9ln((2x-5)(x-2))) ?

The derivative of (4x-9ln((2x-5)(x-2))) is 4ln((2x-5)(x-2))+((4x-9)^2)/((2x-5)(x-2))

What is the first derivative of (4x-9ln((2x-5)(x-2))) ?

The first derivative of (4x-9ln((2x-5)(x-2))) is 4ln((2x-5)(x-2))+((4x-9)^2)/((2x-5)(x-2))

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\frac{d}{d x} ((4 x - 9) ln ((2 x - 5) (x - 2)))

4 ln ((2 x - 5) (x - 2)) + \frac{( 4 x - 9 ) ^{2}}{( 2 x - 5 ) ( x - 2 )}

Solution steps

\frac{d}{d x} ((4 x - 9) ln ((2 x - 5) (x - 2)))

Apply the Product Rule:

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

f = 4 x - 9, g = ln ((2 x - 5) (x - 2))

= \frac{d}{d x} (4 x - 9) ln ((2 x - 5) (x - 2)) + \frac{d}{d x} (ln ((2 x - 5) (x - 2))) (4 x - 9)

\frac{d}{d x} (4 x - 9) = 4

\frac{d}{d x} (ln ((2 x - 5) (x - 2))) = \frac{4 x - 9}{( 2 x - 5 ) ( x - 2 )}

= 4 ln ((2 x - 5) (x - 2)) + \frac{4 x - 9}{( 2 x - 5 ) ( x - 2 )} (4 x - 9)

\frac{4 x - 9}{( 2 x - 5 ) ( x - 2 )} (4 x - 9) = \frac{( 4 x - 9 ) ^{2}}{( 2 x - 5 ) ( x - 2 )}

= 4 ln ((2 x - 5) (x - 2)) + \frac{( 4 x - 9 ) ^{2}}{( 2 x - 5 ) ( x - 2 )}

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

\int 10 (x - 6)^{4} d x

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

2 y^{^{''}} + 8 y^{^{'}} = 0

y = x^{2} - 3 x + 2

What is the derivative of (4x-9ln((2x-5)(x-2))) ?
The derivative of (4x-9ln((2x-5)(x-2))) is 4ln((2x-5)(x-2))+((4x-9)^2)/((2x-5)(x-2))
What is the first derivative of (4x-9ln((2x-5)(x-2))) ?
The first derivative of (4x-9ln((2x-5)(x-2))) is 4ln((2x-5)(x-2))+((4x-9)^2)/((2x-5)(x-2))