derivative y=4tsqrt(t+7)

解

導関数

y = 4 t t + 7

\frac{2 ( 3 t + 14 )}{t + 7}

解答ステップ

\frac{d}{d t} (4 t t + 7)

定数を除去:

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

= 4 \frac{d}{d t} (t t + 7)

積の法則を適用:

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

f = t, g = t + 7

= 4 (\frac{d t}{d t} t + 7 + \frac{d}{d t} (t + 7) t)

\frac{d t}{d t} = 1

\frac{d}{d t} (t + 7) = \frac{1}{2 t + 7}

= 4 (1 \cdot t + 7 + \frac{1}{2 t + 7} t)

簡素化

4 (1 \cdot t + 7 + \frac{1}{2 t + 7} t) : \frac{2 ( 3 t + 14 )}{t + 7}

= \frac{2 ( 3 t + 14 )}{t + 7}