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Beliebt Rechnen >

derivative y=2ln(3)+1/2 ln(x^2+1)

Lösung

ableitung von

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

Lösung

\frac{x}{x ^{2} + 1}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (2 ln (3)) = 0

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

= 0 + \frac{x}{x ^{2} + 1}

Vereinfache

= \frac{x}{x ^{2} + 1}

Graph

Beliebte Beispiele

derivative of 2x(4-x^2^{1/2})

\frac{d}{d x} (2 x (4 - x^{2})^{\frac{1}{2}})

integral of sex^2x

\int se x^{2} x d x

\int k y d y

derivative of (3x^7-7x+11/(2x^3))

\frac{d}{d x} (\frac{3 x ^{7} - 7 x + 11}{2 x ^{3}})

(dy)/(dx)=sqrt(y)cos^2(sqrt(y))

\frac{d y}{d x} = y cos^{2} (y)