d/(dq)(({R}(q))({R}(q)(q^4+1)^5))

Lösung

\frac{d}{d q} ((R (q)) (R (q) (q^{4} + 1)^{5}))

2 R (q) \frac{d}{d q} (R (q)) (q^{4} + 1)^{5} + 20 q^{3} (q^{4} + 1)^{4} R (q)^{2}

Schritte zur Lösung

\frac{d}{d q} ((R (q)) (R (q) (q^{4} + 1)^{5}))

Vereinfache

(R (q)) (R (q) (q^{4} + 1)^{5}) : R (q)^{2} (q^{4} + 1)^{5}

= \frac{d}{d q} (R (q)^{2} (q^{4} + 1)^{5})

Wende die Produktregel an:

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

f = R (q)^{2}, g = (q^{4} + 1)^{5}

= \frac{d}{d q} (R (q)^{2}) (q^{4} + 1)^{5} + \frac{d}{d q} ((q^{4} + 1)^{5}) R (q)^{2}

\frac{d}{d q} (R (q)^{2}) = 2 R (q) \frac{d}{d q} (R (q))

\frac{d}{d q} ((q^{4} + 1)^{5}) = 20 q^{3} (q^{4} + 1)^{4}

= 2 R (q) \frac{d}{d q} (R (q)) (q^{4} + 1)^{5} + 20 q^{3} (q^{4} + 1)^{4} R (q)^{2}

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