derivative t^2(5t+9)^3

解

導関数

t^{2} (5 t + 9)^{3}

2 t (5 t + 9)^{3} + 15 (5 t + 9)^{2} t^{2}

解答ステップ

\frac{d}{d t} (t^{2} (5 t + 9)^{3})

積の法則を適用:

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

f = t^{2}, g = (5 t + 9)^{3}

= \frac{d}{d t} (t^{2}) (5 t + 9)^{3} + \frac{d}{d t} ((5 t + 9)^{3}) t^{2}

\frac{d}{d t} (t^{2}) = 2 t

\frac{d}{d t} ((5 t + 9)^{3}) = 15 (5 t + 9)^{2}

= 2 t (5 t + 9)^{3} + 15 (5 t + 9)^{2} t^{2}