derivative of 1/(sqrt(-25x^2+2y^2-50))

解答

\frac{d}{d x} (\frac{1}{- 25 x ^{2} + 2 y ^{2} - 50})

- \frac{- 25 x + 2 y \frac{d y}{d x}}{( - 25 x ^{2} + 2 y ^{2} - 50 ) ^{\frac{3}{2}}}

求解步骤

\frac{d}{d x} (\frac{1}{- 25 x ^{2} + 2 y ^{2} - 50})

使用指数法则:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} ((- 25 x^{2} + 2 y^{2} - 50)^{- \frac{1}{2}})

使用连锁律:

- \frac{1}{2 ( - 25 x ^{2} + 2 y ^{2} - 50 ) ^{\frac{3}{2}}} \frac{d}{d x} (- 25 x^{2} + 2 y^{2} - 50)

= - \frac{1}{2 ( - 25 x ^{2} + 2 y ^{2} - 50 ) ^{\frac{3}{2}}} \frac{d}{d x} (- 25 x^{2} + 2 y^{2} - 50)

\frac{d}{d x} (- 25 x^{2} + 2 y^{2} - 50) = - 50 x + 4 y \frac{d y}{d x}

= - \frac{1}{2 ( - 25 x ^{2} + 2 y ^{2} - 50 ) ^{\frac{3}{2}}} (- 50 x + 4 y \frac{d y}{d x})

化简

- \frac{1}{2 ( - 25 x ^{2} + 2 y ^{2} - 50 ) ^{\frac{3}{2}}} (- 50 x + 4 y \frac{d y}{d x}) : - \frac{- 25 x + 2 y \frac{d y}{d x}}{( - 25 x ^{2} + 2 y ^{2} - 50 ) ^{\frac{3}{2}}}

= - \frac{- 25 x + 2 y \frac{d y}{d x}}{( - 25 x ^{2} + 2 y ^{2} - 50 ) ^{\frac{3}{2}}}

x \to 4 lim (x + x)

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

s l o p e (6, - 1), (8, 3)

\frac{d}{d x} (\frac{ln ( x )}{x ^{\frac{6}{5}}})

d er i v a t i v e d ln (x) + a x^{n} + b e^{x}