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Beliebt Rechnen >

derivative of ln(x^2+5x)

Lösung

\frac{d}{d x} (ln (x^{2} + 5 x))

Lösung

\frac{2 x + 5}{x ^{2} + 5 x}

Schritte zur Lösung

\frac{d}{d x} (ln (x^{2} + 5 x))

Wende die Kettenregel an:

\frac{1}{x ^{2} + 5 x} \frac{d}{d x} (x^{2} + 5 x)

= \frac{1}{x ^{2} + 5 x} \frac{d}{d x} (x^{2} + 5 x)

\frac{d}{d x} (x^{2} + 5 x) = 2 x + 5

= \frac{1}{x ^{2} + 5 x} (2 x + 5)

Vereinfache

\frac{1}{x ^{2} + 5 x} (2 x + 5) : \frac{2 x + 5}{x ^{2} + 5 x}

= \frac{2 x + 5}{x ^{2} + 5 x}

Graph

Beliebte Beispiele

integral from 0 to 1 of 1/(sqrt(3-2x))

\int_{0}^{1} \frac{1}{3 - 2 x} d x

tangent f(x)=x^2,\at x=4

t an g e n t f (x) = x^{2}, at x = 4

derivative of 2+3e^{-3/x}

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

derivative of (x^4+3x^2-5^4)

\frac{d}{d x} ((x^{4} + 3 x^{2} - 5)^{4})

derivative of 3xe^{5x}

\frac{d}{d x} (3 x e^{5 x})