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

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (8 8 x^{2} + 3)

y^{^{'}} = \frac{3 x}{y + x ^{2} y}, y (0) = - 3

\frac{\partial}{\partial z} (\frac{1}{z})

in v erse l a pl a ce \frac{1}{( s - 2 ) ( s - 4 )}

\frac{d}{d x} (3 3 x^{4} + 5)