derivative cos^2(x)sin^2(x)

Lösung

ableitung von

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}

n = 1 \sum \infty \frac{n !}{10 5 ^{n}}

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

x 1 - y^{2} d x = d y

x \to 0 + lim (ln (- x))

n = 0 \sum \infty \frac{n}{n ^{2} + 1} x^{n}