derivative of cos^2(xtan(x))

Lösung

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

cos (2 x)

Schritte zur Lösung

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

Vereinfache

cos^{2} (x) tan (x) : cos (x) sin (x)

= \frac{d}{d x} (cos (x) sin (x))

Wende die Produktregel an:

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

f = cos (x), g = sin (x)

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

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

\frac{d}{d x} (sin (x)) = cos (x)

= (- sin (x)) sin (x) + cos (x) cos (x)

Vereinfache

(- sin (x)) sin (x) + cos (x) cos (x) : cos (2 x)

= cos (2 x)

\frac{d}{d x} (cot (x) d x)

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

\int \frac{8 + u}{u} d u

\int \frac{x}{e ^{5 x}} d x

d er i v a t i v e \frac{x ^{3}}{6} + \frac{1}{2 x}