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受欢迎的微积分 >

tangent (3x+1)/(x^2+1)

解答

切线

\frac{3 x + 1}{x ^{2} + 1}

解答

y = \frac{- 3 a _{0}^{2} - 2 a _{0} + 3}{( a _{0}^{2} + 1 ) ^{2}} x + \frac{6 a _{0}^{3} + 3 a _{0}^{2} + 1}{( a _{0}^{2} + 1 ) ^{2}}

求解步骤

计算在一般点

x = a_{0}

的切线

找到切点:

(a_{0}, \frac{3 a _{0} + 1}{a _{0}^{2} + 1})

计算

y = \frac{3 x + 1}{x ^{2} + 1}

的斜率:

\frac{d y}{d x} = \frac{- 3 x ^{2} - 2 x + 3}{( x ^{2} + 1 ) ^{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{- 3 a _{0}^{2} - 2 a _{0} + 3}{( a _{0}^{2} + 1 ) ^{2}}

找到斜率 m=

\frac{- 3 a _{0}^{2} - 2 a _{0} + 3}{( a _{0}^{2} + 1 ) ^{2}}

且穿过

(a_{0}, \frac{3 a _{0} + 1}{a _{0}^{2} + 1})

的直线:

y = \frac{- 3 a _{0}^{2} - 2 a _{0} + 3}{( a _{0}^{2} + 1 ) ^{2}} x + \frac{6 a _{0}^{3} + 3 a _{0}^{2} + 1}{( a _{0}^{2} + 1 ) ^{2}}

y = \frac{- 3 a _{0}^{2} - 2 a _{0} + 3}{( a _{0}^{2} + 1 ) ^{2}} x + \frac{6 a _{0}^{3} + 3 a _{0}^{2} + 1}{( a _{0}^{2} + 1 ) ^{2}}

作图

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