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Beliebt Rechnen >

derivative of ln((3x+1(x+2)^2))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

\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)

Vereinfache

\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 )}

Graph

Beliebte Beispiele

derivative of e^{-2x}cos(x)

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

tangent y=3+4x+7xe^x

t an g e n t y = 3 + 4 x + 7 x e^{x}

integral of tan(x)(4cos(x)+8sec(x))

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

(dy)/(dx)+y^5x+6y=0

\frac{d y}{d x} + y^{5} x + 6 y = 0

integral of 1/(x^2sqrt(4-x^2))

\int \frac{1}{x ^{2} 4 - x ^{2}} d x