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

解答

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

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

求解步骤

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

将常数提出:

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

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

使用连锁律:

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

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

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

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

化简

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

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

\int_{0}^{2} a^{\frac{x}{2}} d x

\int - \frac{9}{x} d x

\int_{1}^{5} \frac{x ^{2} + 7}{6 x - x ^{2}} d x

n \to \infty lim (7 n)

\int 0.5