(\partial)/(\partial x)(sqrt(56x^2-8y^2-16x-31)+1-8x)

解

\frac{\partial}{\partial x} (56 x^{2} - 8 y^{2} - 16 x - 31 + 1 - 8 x)

\frac{8 ( 7 x - 1 )}{56 x ^{2} - 16 x - 8 y ^{2} - 31} - 8

解答ステップ

\frac{\partial}{\partial x} (56 x^{2} - 8 y^{2} - 16 x - 31 + 1 - 8 x)

y

を定数として扱う

和/差の法則を適用:

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

= \frac{\partial}{\partial x} (56 x^{2} - 8 y^{2} - 16 x - 31) + \frac{\partial}{\partial x} (1) - \frac{\partial}{\partial x} (8 x)

\frac{\partial}{\partial x} (56 x^{2} - 8 y^{2} - 16 x - 31) = \frac{8 ( 7 x - 1 )}{56 x ^{2} - 8 y ^{2} - 16 x - 31}

\frac{\partial}{\partial x} (1) = 0

\frac{\partial}{\partial x} (8 x) = 8

= \frac{8 ( 7 x - 1 )}{56 x ^{2} - 8 y ^{2} - 16 x - 31} + 0 - 8

簡素化

= \frac{8 ( 7 x - 1 )}{56 x ^{2} - 16 x - 8 y ^{2} - 31} - 8