derivative of (xsin(2x)/(cos(3x)))

Lösung

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

sin (2 x) sec (3 x) + x (2 cos (2 x) sec (3 x) + 3 sec (3 x) tan (3 x) sin (2 x))

Schritte zur Lösung

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

Vereinfache

\frac{x sin ( 2 x )}{cos ( 3 x )} : x sin (2 x) sec (3 x)

= \frac{d}{d x} (x sin (2 x) sec (3 x))

Wende die Produktregel an:

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

f = x, g = sin (2 x) sec (3 x)

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

\frac{d x}{d x} = 1

\frac{d}{d x} (sin (2 x) sec (3 x)) = cos (2 x) \cdot 2 sec (3 x) + sec (3 x) tan (3 x) \cdot 3 sin (2 x)

= 1 \cdot sin (2 x) sec (3 x) + (cos (2 x) \cdot 2 sec (3 x) + sec (3 x) tan (3 x) \cdot 3 sin (2 x)) x

Vereinfache

= sin (2 x) sec (3 x) + x (2 cos (2 x) sec (3 x) + 3 sec (3 x) tan (3 x) sin (2 x))

8 t \frac{d y}{d t} + y = t^{5}

d er i v a t i v e f (x) = x^{2} + 3 x

\int_{- π}^{0} sin (x) + x d x

\frac{d}{d x} (e^{6 x} cos (b x))

d er i v a t i v e (x + y)^{2} - 4 x + y + 10