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受欢迎的微积分 >

tangent (5x-3)^4(2x-7)^{-3}

解答

切线

(5 x - 3)^{4} (2 x - 7)^{- 3}

解答

y = \frac{1250 a _{0}^{4} - 17500 a _{0}^{3} + 28800 a _{0}^{2} - 16740 a _{0} + 3294}{( 2 a _{0} - 7 ) ^{4}} x + \frac{10125 a _{0}^{4} - 15600 a _{0}^{3} + 6210 a _{0}^{2} + 648 a _{0} - 567}{( 2 a _{0} - 7 ) ^{4}}

求解步骤

计算在一般点

x = a_{0}

的切线

找到切点:

(a_{0}, \frac{( 5 a _{0} - 3 ) ^{4}}{( 2 a _{0} - 7 ) ^{3}})

计算

y = (5 x - 3)^{4} (2 x - 7)^{- 3}

的斜率:

\frac{d y}{d x} = \frac{20 ( 5 x - 3 ) ^{3}}{( 2 x - 7 ) ^{3}} - \frac{6 ( 5 x - 3 ) ^{4}}{( 2 x - 7 ) ^{4}}

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{1250 a _{0}^{4} - 17500 a _{0}^{3} + 28800 a _{0}^{2} - 16740 a _{0} + 3294}{( 2 a _{0} - 7 ) ^{4}}

找到斜率 m=

\frac{1250 a _{0}^{4} - 17500 a _{0}^{3} + 28800 a _{0}^{2} - 16740 a _{0} + 3294}{( 2 a _{0} - 7 ) ^{4}}

且穿过

(a_{0}, \frac{( 5 a _{0} - 3 ) ^{4}}{( 2 a _{0} - 7 ) ^{3}})

的直线:

y = \frac{1250 a _{0}^{4} - 17500 a _{0}^{3} + 28800 a _{0}^{2} - 16740 a _{0} + 3294}{( 2 a _{0} - 7 ) ^{4}} x + \frac{10125 a _{0}^{4} - 15600 a _{0}^{3} + 6210 a _{0}^{2} + 648 a _{0} - 567}{( 2 a _{0} - 7 ) ^{4}}

y = \frac{1250 a _{0}^{4} - 17500 a _{0}^{3} + 28800 a _{0}^{2} - 16740 a _{0} + 3294}{( 2 a _{0} - 7 ) ^{4}} x + \frac{10125 a _{0}^{4} - 15600 a _{0}^{3} + 6210 a _{0}^{2} + 648 a _{0} - 567}{( 2 a _{0} - 7 ) ^{4}}

作图

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