What is the derivative of ln((3x+1(x+2)^2)) ?

The derivative of ln((3x+1(x+2)^2)) is (9x+8)/((3x+1)(x+2))

What is the first derivative of ln((3x+1(x+2)^2)) ?

The first derivative of ln((3x+1(x+2)^2)) is (9x+8)/((3x+1)(x+2))

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

\frac{9 x + 8}{( 3 x + 1 ) ( x + 2 )}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} ((3 x + 1) (x + 2)^{2}) = 9 x^{2} + 26 x + 16

= \frac{1}{( 3 x + 1 ) ( x + 2 ) ^{2}} (9 x^{2} + 26 x + 16)

Simplify

\frac{1}{( 3 x + 1 ) ( x + 2 ) ^{2}} (9 x^{2} + 26 x + 16) : \frac{9 x + 8}{( 3 x + 1 ) ( x + 2 )}

= \frac{9 x + 8}{( 3 x + 1 ) ( x + 2 )}

\frac{d}{d x} (x sin (\frac{7}{x}))

\frac{d}{d x} (e^{- 2 x} cos (x))

y = 3 + 4 x + 7 x e^{x}

x^{2} y^{^{''}} + 3 x y^{^{'}} - 35 y = 0

\int tan (x) (4 cos (x) + 8 sec (x)) d x

What is the derivative of ln((3x+1(x+2)^2)) ?
The derivative of ln((3x+1(x+2)^2)) is (9x+8)/((3x+1)(x+2))
What is the first derivative of ln((3x+1(x+2)^2)) ?
The first derivative of ln((3x+1(x+2)^2)) is (9x+8)/((3x+1)(x+2))