derivative of ({Q}(x)k({Q}(x)-70))

Lösung

\frac{d}{d x} ((Q (x)) k (Q (x) - 70))

k (2 Q (x) \frac{d}{d x} (Q (x)) - 70 \frac{d}{d x} (Q (x)))

Schritte zur Lösung

\frac{d}{d x} ((Q (x)) k (Q (x) - 70))

Entferne die Konstante:

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

= k \frac{d}{d x} (Q (x) (Q (x) - 70))

Wende die Produktregel an:

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

f = Q (x), g = Q (x) - 70

= k (\frac{d}{d x} (Q (x)) (Q (x) - 70) + \frac{d}{d x} (Q (x) - 70) Q (x))

\frac{d}{d x} (Q (x) - 70) = \frac{d}{d x} (Q (x))

= k (\frac{d}{d x} (Q (x)) (Q (x) - 70) + \frac{d}{d x} (Q (x)) Q (x))

Multipliziere aus

\frac{d}{d x} (Q (x)) (Q (x) - 70) + \frac{d}{d x} (Q (x)) Q (x) : 2 Q (x) \frac{d}{d x} (Q (x)) - 70 \frac{d}{d x} (Q (x))

= k (2 Q (x) \frac{d}{d x} (Q (x)) - 70 \frac{d}{d x} (Q (x)))

e x p an d \frac{( 5 x + 2 ) ( 7 x - 2 )}{( x - 4 )}

e x p an d \frac{( 2 y - 3 x + 7 ) ( 2 y + 3 x + 1 )}{4}

e x p an d \frac{1 - x ^{5}}{1 - x}

e x p an d \frac{5 ( - x ^{2} + 20 x + 1100 )}{2}

e x p an d \frac{1}{2 ( 8 x + 2 )}