derivative of sin^2(xcot(5x))

Lösung

\frac{d}{d x} (sin^{2} (x) cot (5 x))

sin (2 x) cot (5 x) - 5 csc^{2} (5 x) sin^{2} (x)

Schritte zur Lösung

\frac{d}{d x} (sin^{2} (x) cot (5 x))

Wende die Produktregel an:

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

f = sin^{2} (x), g = cot (5 x)

= \frac{d}{d x} (sin^{2} (x)) cot (5 x) + \frac{d}{d x} (cot (5 x)) sin^{2} (x)

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

\frac{d}{d x} (cot (5 x)) = - csc^{2} (5 x) \cdot 5

= sin (2 x) cot (5 x) + (- csc^{2} (5 x) \cdot 5) sin^{2} (x)

Vereinfache

= sin (2 x) cot (5 x) - 5 csc^{2} (5 x) sin^{2} (x)

in v erse l a pl a ce \frac{4 s - 36}{s ^{2} - 8 s + 15}

s l o p e (0.5) (1)

\frac{d}{d u} (ln (u))

(y^{2} - 2 x y) d x + x^{2} d y = 0

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