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受欢迎的微积分 >

tangent y=(x^2+1)^3(sqrt(x)-1)

解答

切线

y = (x^{2} + 1)^{3} (x - 1)

解答

y = (6 a_{0} (a_{0}^{2} + 1)^{2} (a_{0} - 1) + \frac{( a _{0}^{2} + 1 ) ^{3}}{2 a _{0}}) x - 5 a_{0}^{6} a_{0} + 5 a_{0}^{6} - 9 a_{0}^{4} a_{0} + 9 a_{0}^{4} - 3 a_{0}^{2} a_{0} + 3 a_{0}^{2} + a_{0} - \frac{a _{0} ( a _{0}^{2} + 1 ) ^{3}}{2} - 1

求解步骤

计算在一般点

x = a_{0}

的切线

找到切点:

(a_{0}, (a_{0}^{2} + 1)^{3} (a_{0} - 1))

计算

y = (x^{2} + 1)^{3} (x - 1)

的斜率:

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

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

找到斜率 m=

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

且穿过

(a_{0}, (a_{0}^{2} + 1)^{3} (a_{0} - 1))

的直线:

y = (6 a_{0} (a_{0}^{2} + 1)^{2} (a_{0} - 1) + \frac{( a _{0}^{2} + 1 ) ^{3}}{2 a _{0}}) x - 5 a_{0}^{6} a_{0} + 5 a_{0}^{6} - 9 a_{0}^{4} a_{0} + 9 a_{0}^{4} - 3 a_{0}^{2} a_{0} + 3 a_{0}^{2} + a_{0} - \frac{a _{0} ( a _{0}^{2} + 1 ) ^{3}}{2} - 1

y = (6 a_{0} (a_{0}^{2} + 1)^{2} (a_{0} - 1) + \frac{( a _{0}^{2} + 1 ) ^{3}}{2 a _{0}}) x - 5 a_{0}^{6} a_{0} + 5 a_{0}^{6} - 9 a_{0}^{4} a_{0} + 9 a_{0}^{4} - 3 a_{0}^{2} a_{0} + 3 a_{0}^{2} + a_{0} - \frac{a _{0} ( a _{0}^{2} + 1 ) ^{3}}{2} - 1

作图

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