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Beliebt Rechnen >

derivative of arctan(3/(x+2))

Lösung

\frac{d}{d x} (arctan (\frac{3}{x + 2}))

Lösung

- \frac{3}{x ^{2} + 4 x + 13}

Schritte zur Lösung

\frac{d}{d x} (arctan (\frac{3}{x + 2}))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{( \frac{3}{x + 2} ) ^{2} + 1} (- \frac{3}{( x + 2 ) ^{2}}) : - \frac{3}{x ^{2} + 4 x + 13}

= - \frac{3}{x ^{2} + 4 x + 13}

Graph

Beliebte Beispiele

integral of (sin(x))/(2+cos(x))

\int \frac{sin ( x )}{2 + cos ( x )} d x

tangent f(x)=(x^2+15)(2x+18)

t an g e n t f (x) = (x^{2} + 15) (2 x + 18)

integral of (16)/(1+x^2)

\int \frac{16}{1 + x ^{2}} d x

(dy)/(dx)=2(1-y)

\frac{d y}{d x} = 2 (1 - y)

(\partial)/(\partial y)((-1)/(x^2+y^2))

\frac{\partial}{\partial y} (\frac{- 1}{x ^{2} + y ^{2}})