derivative of 100(y-x^2^2+(1-x)^2)

解答

\frac{d}{d x} (100 (y - x^{2})^{2} + (1 - x)^{2})

200 (y - x^{2}) (\frac{d y}{d x} - 2 x) - 2 (1 - x)

求解步骤

\frac{d}{d x} (100 (y - x^{2})^{2} + (1 - x)^{2})

使用微分加减法定则:

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

= \frac{d}{d x} (100 (y - x^{2})^{2}) + \frac{d}{d x} ((1 - x)^{2})

\frac{d}{d x} (100 (y - x^{2})^{2}) = 200 (y - x^{2}) (\frac{d y}{d x} - 2 x)

\frac{d}{d x} ((1 - x)^{2}) = - 2 (1 - x)

= 200 (y - x^{2}) (\frac{d y}{d x} - 2 x) - 2 (1 - x)

x \to 0 lim (\frac{x}{- x})

\int (x^{2} + \frac{1}{4} y^{2} + 3) d x

\frac{d y}{d t} = 0.03 y + 3600

\frac{\partial}{\partial x} (x^{\frac{3}{2}})

\int e^{b x} d x