derivative of sqrt(17x^2+9)

解

\frac{d}{d x} (17 x^{2} + 9)

\frac{17 x}{17 x ^{2} + 9}

解答ステップ

\frac{d}{d x} (17 x^{2} + 9)

連鎖法則を適用:

\frac{1}{2 17 x ^{2} + 9} \frac{d}{d x} (17 x^{2} + 9)

= \frac{1}{2 17 x ^{2} + 9} \frac{d}{d x} (17 x^{2} + 9)

\frac{d}{d x} (17 x^{2} + 9) = 34 x

= \frac{1}{2 17 x ^{2} + 9} \cdot 34 x

簡素化

\frac{1}{2 17 x ^{2} + 9} \cdot 34 x : \frac{17 x}{17 x ^{2} + 9}

= \frac{17 x}{17 x ^{2} + 9}