derivative of 12x^3cos(x^4)

Lösung

\frac{d}{d x} (12 x^{3} cos (x^{4}))

12 (3 x^{2} cos (x^{4}) - 4 x^{6} sin (x^{4}))

Schritte zur Lösung

\frac{d}{d x} (12 x^{3} cos (x^{4}))

Entferne die Konstante:

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

= 12 \frac{d}{d x} (x^{3} cos (x^{4}))

Wende die Produktregel an:

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

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

= 12 (\frac{d}{d x} (x^{3}) cos (x^{4}) + \frac{d}{d x} (cos (x^{4})) x^{3})

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

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

= 12 (3 x^{2} cos (x^{4}) + (- sin (x^{4}) \cdot 4 x^{3}) x^{3})

Vereinfache

12 (3 x^{2} cos (x^{4}) + (- sin (x^{4}) \cdot 4 x^{3}) x^{3}) : 12 (3 x^{2} cos (x^{4}) - 4 x^{6} sin (x^{4}))

= 12 (3 x^{2} cos (x^{4}) - 4 x^{6} sin (x^{4}))

\frac{\partial}{\partial x} (\frac{1}{2} x^{2})

θ \to - \frac{π}{2} - lim (sec (θ))

y^{^{''}} + 6 y^{^{'}} + 18 y = 0

y \to 0 lim (cot (5 y))

\frac{\partial}{\partial x} (\frac{e ^{x}}{y + x ^{2}})