derivative cos(3x^2+4)*6x

Lösung

ableitung von

cos (3 x^{2} + 4) \cdot 6 x

6 (- 6 x^{2} sin (3 x^{2} + 4) + cos (3 x^{2} + 4))

Schritte zur Lösung

\frac{d}{d x} (cos (3 x^{2} + 4) \cdot 6 x)

Entferne die Konstante:

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

= 6 \frac{d}{d x} (cos (3 x^{2} + 4) x)

Wende die Produktregel an:

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

f = cos (3 x^{2} + 4), g = x

= 6 (\frac{d}{d x} (cos (3 x^{2} + 4)) x + \frac{d x}{d x} cos (3 x^{2} + 4))

\frac{d}{d x} (cos (3 x^{2} + 4)) = - sin (3 x^{2} + 4) \cdot 6 x

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

= 6 ((- sin (3 x^{2} + 4) \cdot 6 x) x + 1 \cdot cos (3 x^{2} + 4))

Vereinfache

6 ((- sin (3 x^{2} + 4) \cdot 6 x) x + 1 \cdot cos (3 x^{2} + 4)) : 6 (- 6 x^{2} sin (3 x^{2} + 4) + cos (3 x^{2} + 4))

= 6 (- 6 x^{2} sin (3 x^{2} + 4) + cos (3 x^{2} + 4))

\int \frac{1}{3 x ^{2} + 6 x + 6} d x

a re a sin (x), x = 0, y = 0, x = \frac{π}{6}

y^{^{''}} + 4 y^{^{'}} + 4 y = x \cdot cos (2 x) + 3 e^{- 2 x}

\frac{d x}{d t} + 3 x = e^{- 2 t}

x \to 0 - lim ((1 + x)^{\frac{1}{x}})