derivative of (x+2^2+(10-3x)^2)

解

\frac{d}{d x} ((x + 2)^{2} + (10 - 3 x)^{2})

20 x - 56

解答ステップ

\frac{d}{d x} ((x + 2)^{2} + (10 - 3 x)^{2})

簡素化

(x + 2)^{2} + (10 - 3 x)^{2} : 10 x^{2} - 56 x + 104

= \frac{d}{d x} (10 x^{2} - 56 x + 104)

和/差の法則を適用:

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

= \frac{d}{d x} (10 x^{2}) - \frac{d}{d x} (56 x) + \frac{d}{d x} (104)

\frac{d}{d x} (10 x^{2}) = 20 x

\frac{d}{d x} (56 x) = 56

\frac{d}{d x} (104) = 0

= 20 x - 56 + 0

簡素化

= 20 x - 56