derivative of sin^2(xcos^3(x))

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = sin^{2} (x), g = cos^{3} (x)

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

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

\frac{d}{d x} (cos^{3} (x)) = - 3 cos^{2} (x) sin (x)

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

Vereinfache

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

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

x \to 0 lim (x sin (\frac{4}{x}))

y^{^{'}} + y + 2 cos (x) = 0

\int_{4}^{6} \frac{1}{x} d x

x \to - 1 lim (x^{3} - 4 x + 1)

n = 10000 \sum \infty \frac{1}{n}