derivative of xtan(2sqrt(x))

Lösung

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

tan (2 x) + x sec^{2} (2 x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = tan (2 x)

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

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

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

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

Vereinfache

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

= tan (2 x) + x sec^{2} (2 x)

\frac{\partial}{\partial x} (sin (x^{3}))

x \to 3 + lim (\frac{2 x + 1}{x - 3})

\int sin (4 π t) d t

\int 2 t^{4} + 2 d t

\int cos^{2} (x) sin (2 x) d x