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tangent x/(x^2+4)

解答

切线

\frac{x}{x ^{2} + 4}

解答

y = \frac{- a _{0}^{2} + 4}{( a _{0}^{2} + 4 ) ^{2}} x + \frac{2 a _{0}^{3}}{( a _{0}^{2} + 4 ) ^{2}}

求解步骤

计算在一般点

x = a_{0}

的切线

找到切点:

(a_{0}, \frac{a _{0}}{a _{0}^{2} + 4})

计算

y = \frac{x}{x ^{2} + 4}

的斜率:

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

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = \frac{- a _{0}^{2} + 4}{( a _{0}^{2} + 4 ) ^{2}}

找到斜率 m=

\frac{- a _{0}^{2} + 4}{( a _{0}^{2} + 4 ) ^{2}}

且穿过

(a_{0}, \frac{a _{0}}{a _{0}^{2} + 4})

的直线:

y = \frac{- a _{0}^{2} + 4}{( a _{0}^{2} + 4 ) ^{2}} x + \frac{2 a _{0}^{3}}{( a _{0}^{2} + 4 ) ^{2}}

y = \frac{- a _{0}^{2} + 4}{( a _{0}^{2} + 4 ) ^{2}} x + \frac{2 a _{0}^{3}}{( a _{0}^{2} + 4 ) ^{2}}

作图

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