derivative of (1+2sin(x)sin(x))

Lösung

\frac{d}{d x} ((1 + 2 sin (x)) sin (x))

cos (x) (1 + 2 sin (x)) + sin (2 x)

Schritte zur Lösung

\frac{d}{d x} ((1 + 2 sin (x)) sin (x))

Wende die Produktregel an:

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

f = 1 + 2 sin (x), g = sin (x)

= \frac{d}{d x} (1 + 2 sin (x)) sin (x) + \frac{d}{d x} (sin (x)) (1 + 2 sin (x))

\frac{d}{d x} (1 + 2 sin (x)) = 2 cos (x)

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

= 2 cos (x) sin (x) + cos (x) (1 + 2 sin (x))

Verwende die Doppelwinkelidentität:

2 sin (x) cos (x) = sin (2 x)

= cos (x) (1 + 2 sin (x)) + sin (2 x)

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

\int_{0}^{1} 2 π (x + 8) x^{2} d x

x \to - 2 lim (- 3 x^{2} - 6 x + 4)

d er i v a t i v e sin (5) x^{2}

\frac{d}{d x} (\frac{3 x - 5}{2 x + 4})