What is the derivative of (4x-21ln((2x-11)(x-5))) ?

The derivative of (4x-21ln((2x-11)(x-5))) is 4ln((2x-11)(x-5))+((4x-21)^2)/((2x-11)(x-5))

What is the first derivative of (4x-21ln((2x-11)(x-5))) ?

The first derivative of (4x-21ln((2x-11)(x-5))) is 4ln((2x-11)(x-5))+((4x-21)^2)/((2x-11)(x-5))

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\frac{d}{d x} ((4 x - 21) ln ((2 x - 11) (x - 5)))

4 ln ((2 x - 11) (x - 5)) + \frac{( 4 x - 21 ) ^{2}}{( 2 x - 11 ) ( x - 5 )}

Solution steps

\frac{d}{d x} ((4 x - 21) ln ((2 x - 11) (x - 5)))

Apply the Product Rule:

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

f = 4 x - 21, g = ln ((2 x - 11) (x - 5))

= \frac{d}{d x} (4 x - 21) ln ((2 x - 11) (x - 5)) + \frac{d}{d x} (ln ((2 x - 11) (x - 5))) (4 x - 21)

\frac{d}{d x} (4 x - 21) = 4

\frac{d}{d x} (ln ((2 x - 11) (x - 5))) = \frac{4 x - 21}{( 2 x - 11 ) ( x - 5 )}

= 4 ln ((2 x - 11) (x - 5)) + \frac{4 x - 21}{( 2 x - 11 ) ( x - 5 )} (4 x - 21)

\frac{4 x - 21}{( 2 x - 11 ) ( x - 5 )} (4 x - 21) = \frac{( 4 x - 21 ) ^{2}}{( 2 x - 11 ) ( x - 5 )}

= 4 ln ((2 x - 11) (x - 5)) + \frac{( 4 x - 21 ) ^{2}}{( 2 x - 11 ) ( x - 5 )}

\frac{2}{x ^{2}}, 2

\int \frac{x ^{2} - 18 x - 1}{( x - 1 ) ^{2} ( x ^{2} + 1 )} d x

(x + y)^{2} d x + (2 x y + x^{2} - 1) d y = 0, y (1) = 1

\frac{\partial}{\partial y} (- sin (x y) x)

\frac{\partial}{\partial y} (5 x (4 + y)^{- 1})

What is the derivative of (4x-21ln((2x-11)(x-5))) ?
The derivative of (4x-21ln((2x-11)(x-5))) is 4ln((2x-11)(x-5))+((4x-21)^2)/((2x-11)(x-5))
What is the first derivative of (4x-21ln((2x-11)(x-5))) ?
The first derivative of (4x-21ln((2x-11)(x-5))) is 4ln((2x-11)(x-5))+((4x-21)^2)/((2x-11)(x-5))