derivative 2(sin(x^2)+2x^2cos(x^2))

Lösung

ableitung von

2 (sin (x^{2}) + 2 x^{2} cos (x^{2}))

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Multipliziere aus

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

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

t an g e n t f (x) = \frac{1}{3 x}, at x = 9

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