derivative of sqrt(y-x)n(y+x)

解答

\frac{d}{d x} (y - x n (y + x))

\frac{n ( - x \frac{d y}{d x} - 3 x + 3 y \frac{d y}{d x} + y )}{2 y - x}

求解步骤

\frac{d}{d x} (y - x n (y + x))

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= n \frac{d}{d x} (y - x (y + x))

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y - x, g = y + x

= n (\frac{d}{d x} (y - x) (y + x) + \frac{d}{d x} (y + x) y - x)

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

\frac{d}{d x} (y + x) = \frac{d y}{d x} + 1

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

化简

n (\frac{\frac{d y}{d x} - 1}{2 y - x} (y + x) + (\frac{d y}{d x} + 1) y - x) : \frac{n ( - x \frac{d y}{d x} - 3 x + 3 y \frac{d y}{d x} + y )}{2 y - x}

= \frac{n ( - x \frac{d y}{d x} - 3 x + 3 y \frac{d y}{d x} + y )}{2 y - x}

\frac{\partial}{\partial y} (x - y - 1)

x \to 0 lim (e^{- x} cos (x))

\frac{d ^{2}}{d x ^{2}} (sec (x))

e^{e^{x}} \to 0 + lim (\frac{e ^{e^{x} - 2}}{e ^{e^{x}}})

d er i v a t i v e (x - 1) (x^{2} - 8 x + 7)