derivative 7(sin(x^2)+2x^2cos(x^2))

Lösung

ableitung von

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

7 (6 x cos (x^{2}) - 4 x^{3} sin (x^{2}))

Schritte zur Lösung

\frac{d}{d x} (7 (sin (x^{2}) + 2 x^{2} cos (x^{2})))

Entferne die Konstante:

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

= 7 \frac{d}{d x} (sin (x^{2}) + 2 x^{2} cos (x^{2}))

Wende die Summen-/Differenzregel an:

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

= 7 (\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}))

= 7 (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})

= 7 (6 x cos (x^{2}) - 4 x^{3} sin (x^{2}))

\frac{d}{d x} (5 x^{3} y^{2} + x^{2} sin (y^{2}))

x \to 0 lim (- 10 x)

\frac{\partial}{\partial x} (x^{2} sin (x))

\int \frac{1}{2 x x} d x

\int ln (x) x^{13} d x