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Beliebt Rechnen >

derivative (1+cos^2(x))^3

Lösung

ableitung von

(1 + cos^{2} (x))^{3}

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

= 3 (1 + cos^{2} (x))^{2} (- sin (2 x))

Vereinfache

= - 3 sin (2 x) (1 + cos^{2} (x))^{2}

Graph

Beliebte Beispiele

(1+x^2)(dy)/(dx)=2xy+1

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

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

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

derivative of (16/(x^2))

\frac{d}{d x} (\frac{16}{x ^{2}})

(\partial)/(\partial y)(xy^3+x^2)

\frac{\partial}{\partial y} (x y^{3} + x^{2})

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

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