derivative f(x)=sqrt(5x^2+3x+8)

解

導関数

f (x) = 5 x^{2} + 3 x + 8

\frac{10 x + 3}{2 5 x ^{2} + 3 x + 8}

解答ステップ

\frac{d}{d x} (5 x^{2} + 3 x + 8)

連鎖法則を適用:

\frac{1}{2 5 x ^{2} + 3 x + 8} \frac{d}{d x} (5 x^{2} + 3 x + 8)

= \frac{1}{2 5 x ^{2} + 3 x + 8} \frac{d}{d x} (5 x^{2} + 3 x + 8)

\frac{d}{d x} (5 x^{2} + 3 x + 8) = 10 x + 3

= \frac{1}{2 5 x ^{2} + 3 x + 8} (10 x + 3)

簡素化

\frac{1}{2 5 x ^{2} + 3 x + 8} (10 x + 3) : \frac{10 x + 3}{2 5 x ^{2} + 3 x + 8}

= \frac{10 x + 3}{2 5 x ^{2} + 3 x + 8}