(\partial)/(\partial x)(-ksqrt(p(x)gx))

解答

\frac{\partial}{\partial x} (- k p (x) gx)

- \frac{k g ( x \frac{\partial}{\partial x} ( p ( x ) ) + p ( x ) )}{2 x p ( x )}

求解步骤

\frac{\partial}{\partial x} (- k p (x) gx)

将常数提出:

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

= - k \frac{\partial}{\partial x} (p (x) gx)

使用连锁律:

\frac{1}{2 p ( x ) gx} \frac{\partial}{\partial x} (p (x) gx)

= \frac{1}{2 p ( x ) gx} \frac{\partial}{\partial x} (p (x) gx)

\frac{\partial}{\partial x} (p (x) gx) = g (x \frac{\partial}{\partial x} (p (x)) + p (x))

= - k \frac{1}{2 p ( x ) gx} g (x \frac{\partial}{\partial x} (p (x)) + p (x))

化简

- k \frac{1}{2 p ( x ) gx} g (x \frac{\partial}{\partial x} (p (x)) + p (x)) : - \frac{k g ( x \frac{\partial}{\partial x} ( p ( x ) ) + p ( x ) )}{2 x p ( x )}

= - \frac{k g ( x \frac{\partial}{\partial x} ( p ( x ) ) + p ( x ) )}{2 x p ( x )}

d er i v a t i v e y = arcsin (x) - 1 - x^{2}

\frac{d ^{2}}{d x ^{2}} (\frac{x}{x + 7})

t an g e n t f (x) = x + \frac{3}{x}, at x = 4

\frac{d}{d x} (\frac{x ^{2}}{x + 4})

s l o p e in t erce pt (15, 0), (0, - 2)