derivative g(x)= 7/4 x^2-3x+12

解

導関数

g (x) = \frac{7}{4} x^{2} - 3 x + 12

\frac{7 x}{2} - 3

解答ステップ

\frac{d}{d x} (\frac{7}{4} x^{2} - 3 x + 12)

簡素化

\frac{7}{4} x^{2} - 3 x + 12 : \frac{7 x ^{2}}{4} - 3 x + 12

= \frac{d}{d x} (\frac{7 x ^{2}}{4} - 3 x + 12)

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{7 x ^{2}}{4}) - \frac{d}{d x} (3 x) + \frac{d}{d x} (12)

\frac{d}{d x} (\frac{7 x ^{2}}{4}) = \frac{7 x}{2}

\frac{d}{d x} (3 x) = 3

\frac{d}{d x} (12) = 0

= \frac{7 x}{2} - 3 + 0

簡素化

= \frac{7 x}{2} - 3