derivative of 4sqrt(9x^2+5)

解

\frac{d}{d x} (4 9 x^{2} + 5)

\frac{36 x}{9 x ^{2} + 5}

解答ステップ

\frac{d}{d x} (4 9 x^{2} + 5)

定数を除去:

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

= 4 \frac{d}{d x} (9 x^{2} + 5)

連鎖法則を適用:

\frac{1}{2 9 x ^{2} + 5} \frac{d}{d x} (9 x^{2} + 5)

= \frac{1}{2 9 x ^{2} + 5} \frac{d}{d x} (9 x^{2} + 5)

\frac{d}{d x} (9 x^{2} + 5) = 18 x

= 4 \cdot \frac{1}{2 9 x ^{2} + 5} \cdot 18 x

簡素化

4 \cdot \frac{1}{2 9 x ^{2} + 5} \cdot 18 x : \frac{36 x}{9 x ^{2} + 5}

= \frac{36 x}{9 x ^{2} + 5}