derivative of 1/2 tan(xsin(2x))

Lösung

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

sin (2 x)

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Produktregel an:

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

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

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

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

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

= \frac{1}{2} (sec^{2} (x) sin (2 x) + cos (2 x) \cdot 2 tan (x))

Vereinfache

\frac{1}{2} (sec^{2} (x) sin (2 x) + cos (2 x) \cdot 2 tan (x)) : sin (2 x)

= sin (2 x)

y^{^{''}} + 7 y^{^{'}} + 10 y = 14 x e^{3 x}

im pl i c i t \frac{d u}{d v}, u + v = 5

\int (\frac{1}{3} e^{x + 3} + \frac{3}{x} - 5) d x

\int \frac{x ^{2} - 11 x - 18}{x ( x ^{2} + 3 x + 3 )} d x

\frac{\partial}{\partial x} (5 x y - 4 x^{2} y)