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

解答

\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

求解步骤

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

将

y

视为常数

使用微分加减法定则:

(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

化简

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

f (x) = 1 + x

\int \frac{1}{x ^{1 + c}} d x

\int \frac{- 5 x ^{2}}{x ^{4} - 1} d x

\frac{\partial}{\partial t} (cos^{2} (t))

x \to 0 - lim (2 x + c)