derivative of (y^3c(x-c)^2)

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = y^{3}, g = (x - c)^{2}

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

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

\frac{d}{d x} ((x - c)^{2}) = 2 (x - c)

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

e x p an d (x^{2} - 2 x - 3)^{5}

e x p an d (8 x - 20) \circ

e x p an d \frac{4 x}{( 79 - x ) ( 21 - x )}

e x p an d 20 x^{21} x^{22} x^{23}

e x p an d \frac{2 ( 5 + 10 )}{5}