d/(dQ)((T{R}(T,Q))(75Q-4Q^2))

Lösung

\frac{d}{d Q} ((T R (T, Q)) (75 Q - 4 Q^{2}))

T (\frac{d}{d Q} (R (T, Q)) (75 Q - 4 Q^{2}) + (75 - 8 Q) R (T, Q))

Schritte zur Lösung

\frac{d}{d Q} ((T R (T, Q)) (75 Q - 4 Q^{2}))

Behandle

T

als Konstante

Entferne die Konstante:

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

= T \frac{d}{d Q} (R (T, Q) (75 Q - 4 Q^{2}))

Wende die Produktregel an:

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

f = R (T, Q), g = 75 Q - 4 Q^{2}

= T (\frac{d}{d Q} (R (T, Q)) (75 Q - 4 Q^{2}) + \frac{d}{d Q} (75 Q - 4 Q^{2}) R (T, Q))

\frac{d}{d Q} (75 Q - 4 Q^{2}) = 75 - 8 Q

= T (\frac{d}{d Q} (R (T, Q)) (75 Q - 4 Q^{2}) + (75 - 8 Q) R (T, Q))

e x p an d (2 y^{2} + 3 x y - 2 y + 6 x) d x

s im pl i f y (x) (x - 5)

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

\frac{d}{d t} ((w) (cos (t) sin (t) + t))

e x p an d n^{2} (1 - cos (\frac{1}{n}))