derivative of (xsin(2x)^{3/2})

Lösung

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

\frac{3 ( sin ( 2 x ) + 2 x cos ( 2 x ) ) ( x sin ( 2 x ) ) ^{\frac{1}{2}}}{2}

Schritte zur Lösung

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

Wende die Kettenregel an:

\frac{3 ( x sin ( 2 x ) ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (x sin (2 x))

= \frac{3 ( x sin ( 2 x ) ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (x sin (2 x))

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

= \frac{3 ( x sin ( 2 x ) ) ^{\frac{1}{2}}}{2} (sin (2 x) + 2 x cos (2 x))

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 ( sin ( 2 x ) + 2 x cos ( 2 x ) ) ( x sin ( 2 x ) ) ^{\frac{1}{2}}}{2}

\int \frac{( x + 16 )}{( x ^{2} + 2 x - 8 )} d x

\frac{\partial}{\partial α} (K (α) (α)^{α} L^{1 - α})

t an g e n t y = 11 x^{2}, (- 2, 44)

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

t a y l or e^{- 5 x}