derivative of cos^2(xsin^2(x))

Lösung

\frac{d}{d x} (cos^{2} (x) sin^{2} (x))

\frac{sin ( 4 x )}{2}

Schritte zur Lösung

\frac{d}{d x} (cos^{2} (x) sin^{2} (x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cos^{2} (x), g = sin^{2} (x)

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

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

\frac{d}{d x} (sin^{2} (x)) = sin (2 x)

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

Vereinfache

(- sin (2 x)) sin^{2} (x) + sin (2 x) cos^{2} (x) : \frac{sin ( 4 x )}{2}

= \frac{sin ( 4 x )}{2}

\int 9 r cos (r) d r

d er i v a t i v e y = x^{4 x}

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

x \to - 2 lim (x + 1)

n = 1 \sum \infty 1 \cdot (\frac{1}{5})^{n}