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受欢迎的微积分 >

tangent y=((x+5)^5)/(7x-5)

解答

切线

y = \frac{( x + 5 ) ^{5}}{7 x - 5}

解答

y = \frac{28 a _{0}^{5} + 500 a _{0}^{4} + 3000 a _{0}^{3} + 5000 a _{0}^{2} - 12500 a _{0} - 37500}{( 7 a _{0} - 5 ) ^{2}} x + \frac{- 21 a _{0}^{6} - 330 a _{0}^{5} - 1375 a _{0}^{4} + 2500 a _{0}^{3} + 28125 a _{0}^{2} + 43750 a _{0} - 15625}{( 7 a _{0} - 5 ) ^{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} + 5 ) ^{5}}{7 a _{0} - 5})

计算

y = \frac{( x + 5 ) ^{5}}{7 x - 5}

的斜率:

\frac{d y}{d x} = \frac{5 ( x + 5 ) ^{4} ( 7 x - 5 ) - 7 ( x + 5 ) ^{5}}{( 7 x - 5 ) ^{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{28 a _{0}^{5} + 500 a _{0}^{4} + 3000 a _{0}^{3} + 5000 a _{0}^{2} - 12500 a _{0} - 37500}{( 7 a _{0} - 5 ) ^{2}}

找到斜率 m=

\frac{28 a _{0}^{5} + 500 a _{0}^{4} + 3000 a _{0}^{3} + 5000 a _{0}^{2} - 12500 a _{0} - 37500}{( 7 a _{0} - 5 ) ^{2}}

且穿过

(a_{0}, \frac{( a _{0} + 5 ) ^{5}}{7 a _{0} - 5})

的直线:

y = \frac{28 a _{0}^{5} + 500 a _{0}^{4} + 3000 a _{0}^{3} + 5000 a _{0}^{2} - 12500 a _{0} - 37500}{( 7 a _{0} - 5 ) ^{2}} x + \frac{- 21 a _{0}^{6} - 330 a _{0}^{5} - 1375 a _{0}^{4} + 2500 a _{0}^{3} + 28125 a _{0}^{2} + 43750 a _{0} - 15625}{( 7 a _{0} - 5 ) ^{2}}

y = \frac{28 a _{0}^{5} + 500 a _{0}^{4} + 3000 a _{0}^{3} + 5000 a _{0}^{2} - 12500 a _{0} - 37500}{( 7 a _{0} - 5 ) ^{2}} x + \frac{- 21 a _{0}^{6} - 330 a _{0}^{5} - 1375 a _{0}^{4} + 2500 a _{0}^{3} + 28125 a _{0}^{2} + 43750 a _{0} - 15625}{( 7 a _{0} - 5 ) ^{2}}

作图

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