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Beliebt Rechnen >

(arctan(cos(x)))^'

Lösung

(arctan (cos (x)))^{^{'}}

Lösung

- \frac{sin ( x )}{cos ^{2} ( x ) + 1}

Schritte zur Lösung

(arctan (cos (x)))^{'}

Wende die Kettenregel an:

\frac{1}{( cos ( x ) ) ^{2} + 1} (cos (x))^{'}

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

(cos (x))^{'} = - sin (x)

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

Vereinfache

\frac{1}{cos ^{2} ( x ) + 1} (- sin (x)) : - \frac{sin ( x )}{cos ^{2} ( x ) + 1}

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

Graph

Beliebte Beispiele

y^{''}-y^'-6y=20e^{-2x}

y^{^{''}} - y^{^{'}} - 6 y = 20 e^{- 2 x}

2y^{'''}+3y^{''}-8y^'+3y=0

2 y^{^{'''}} + 3 y^{^{''}} - 8 y^{^{'}} + 3 y = 0

derivative of sqrt(x^2+1)-x

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

limit as x approaches 3 of x+2

x \to 3 lim (x + 2)

tangent f(x)=x^2+4x

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