derivative f(x)=tan(2x)*sin(2x)

Lösung

ableitung von

f (x) = tan (2 x) \cdot sin (2 x)

2 sin (2 x) + 2 sec (2 x) tan (2 x)

Schritte zur Lösung

\frac{d}{d x} (tan (2 x) sin (2 x))

Wende die Produktregel an:

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

f = tan (2 x), g = sin (2 x)

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

\frac{d}{d x} (tan (2 x)) = sec^{2} (2 x) \cdot 2

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

= sec^{2} (2 x) \cdot 2 sin (2 x) + cos (2 x) \cdot 2 tan (2 x)

Vereinfache

sec^{2} (2 x) \cdot 2 sin (2 x) + cos (2 x) \cdot 2 tan (2 x) : 2 sin (2 x) + 2 sec (2 x) tan (2 x)

= 2 sin (2 x) + 2 sec (2 x) tan (2 x)

\int_{- 3}^{3} (18 - 2 x^{2}) d x

\int x^{3} e^{x^{4}} d x

6 y^{^{''}} + 12 y^{^{'}} - 18 y = 0

\frac{\partial}{\partial x} ((x - 2) (x^{2} + 4))

x v^{'} + v = - \frac{4 - v + v ^{2}}{1 - v + 4 v ^{2}}