d/(dq)(({R}(q))(q^4+1)^7)

Lösung

\frac{d}{d q} ((R (q)) (q^{4} + 1)^{7})

\frac{d}{d q} (R (q)) (q^{4} + 1)^{7} + 28 q^{3} (q^{4} + 1)^{6} R (q)

Schritte zur Lösung

\frac{d}{d q} ((R (q)) (q^{4} + 1)^{7})

Wende die Produktregel an:

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

f = R (q), g = (q^{4} + 1)^{7}

= \frac{d}{d q} (R (q)) (q^{4} + 1)^{7} + \frac{d}{d q} ((q^{4} + 1)^{7}) R (q)

\frac{d}{d q} ((q^{4} + 1)^{7}) = 28 q^{3} (q^{4} + 1)^{6}

= \frac{d}{d q} (R (q)) (q^{4} + 1)^{7} + 28 q^{3} (q^{4} + 1)^{6} R (q)

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e x p an d \frac{2 ( x + h ) + 3 - 2 x + 3}{h}