derivative of (2x-y^4-y^3-8)

Lösung

\frac{d}{d x} ((2 x - y)^{4} - y^{3} - 8)

4 (2 x - y)^{3} (- \frac{d y}{d x} + 2) - 3 y^{2} \frac{d y}{d x}

Schritte zur Lösung

\frac{d}{d x} ((2 x - y)^{4} - y^{3} - 8)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} ((2 x - y)^{4}) - \frac{d}{d x} (y^{3}) - \frac{d}{d x} (8)

\frac{d}{d x} ((2 x - y)^{4}) = 4 (2 x - y)^{3} (2 - \frac{d y}{d x})

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

\frac{d}{d x} (8) = 0

= 4 (2 x - y)^{3} (2 - \frac{d y}{d x}) - 3 y^{2} \frac{d y}{d x} - 0

Vereinfache

= 4 (2 x - y)^{3} (- \frac{d y}{d x} + 2) - 3 y^{2} \frac{d y}{d x}

e x p an d t^{3} \cdot t^{4}

e x p an d lo g_{21} (81)

e x p an d \frac{x ( x + 2 )}{2 ( x + 1 )}

e x p an d 2 (x - 3 π + 2 π^{2})

e x p an d - 12 x + 27 x