What is the derivative of ln((6x+4(3x^2+2))) ?

The derivative of ln((6x+4(3x^2+2))) is (3(9x^2+4x+2))/((3x+2)(3x^2+2))

What is the first derivative of ln((6x+4(3x^2+2))) ?

The first derivative of ln((6x+4(3x^2+2))) is (3(9x^2+4x+2))/((3x+2)(3x^2+2))

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\frac{d}{d x} (ln ((6 x + 4) (3 x^{2} + 2)))

\frac{3 ( 9 x ^{2} + 4 x + 2 )}{( 3 x + 2 ) ( 3 x ^{2} + 2 )}

Solution steps

\frac{d}{d x} (ln ((6 x + 4) (3 x^{2} + 2)))

Apply the chain rule:

\frac{1}{( 6 x + 4 ) ( 3 x ^{2} + 2 )} \frac{d}{d x} ((6 x + 4) (3 x^{2} + 2))

= \frac{1}{( 6 x + 4 ) ( 3 x ^{2} + 2 )} \frac{d}{d x} ((6 x + 4) (3 x^{2} + 2))

\frac{d}{d x} ((6 x + 4) (3 x^{2} + 2)) = 54 x^{2} + 24 x + 12

= \frac{1}{( 6 x + 4 ) ( 3 x ^{2} + 2 )} (54 x^{2} + 24 x + 12)

Simplify

\frac{1}{( 6 x + 4 ) ( 3 x ^{2} + 2 )} (54 x^{2} + 24 x + 12) : \frac{3 ( 9 x ^{2} + 4 x + 2 )}{( 3 x + 2 ) ( 3 x ^{2} + 2 )}

= \frac{3 ( 9 x ^{2} + 4 x + 2 )}{( 3 x + 2 ) ( 3 x ^{2} + 2 )}

What is the derivative of ln((6x+4(3x^2+2))) ?
The derivative of ln((6x+4(3x^2+2))) is (3(9x^2+4x+2))/((3x+2)(3x^2+2))
What is the first derivative of ln((6x+4(3x^2+2))) ?
The first derivative of ln((6x+4(3x^2+2))) is (3(9x^2+4x+2))/((3x+2)(3x^2+2))