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受欢迎的微积分 >

tangent \sqrt[5]{2x^3+8x}(2.2)

解答

切线

5 2 x^{3} + 8 x (2.2)

解答

y = \frac{0.44 ( 6 a _{0}^{2} + 8 )}{( 2 a _{0}^{3} + 8 a _{0} ) ^{\frac{4}{5}}} x + \frac{220 5 2 a _{0}^{3} + 8 a _{0} ( 2 a _{0}^{3} + 8 a _{0} ) ^{\frac{4}{5}} - 44 a _{0} ( 6 a _{0}^{2} + 8 )}{100 ( 2 a _{0}^{3} + 8 a _{0} ) ^{\frac{4}{5}}}

求解步骤

计算在一般点

x = a_{0}

的切线

找到切点:

(a_{0}, 5 2 a_{0}^{3} + 8 a_{0} \cdot 2.2)

计算

y = 5 2 x^{3} + 8 x 2.2

的斜率:

\frac{d y}{d x} = \frac{0.44 ( 6 x ^{2} + 8 )}{( 2 x ^{3} + 8 x ) ^{\frac{4}{5}}}

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{0.44 ( 6 a _{0}^{2} + 8 )}{( 2 a _{0}^{3} + 8 a _{0} ) ^{\frac{4}{5}}}

找到斜率 m=

\frac{0.44 ( 6 a _{0}^{2} + 8 )}{( 2 a _{0}^{3} + 8 a _{0} ) ^{\frac{4}{5}}}

且穿过

(a_{0}, 5 2 a_{0}^{3} + 8 a_{0} 2.2)

的直线:

y = \frac{0.44 ( 6 a _{0}^{2} + 8 )}{( 2 a _{0}^{3} + 8 a _{0} ) ^{\frac{4}{5}}} x + \frac{220 5 2 a _{0}^{3} + 8 a _{0} ( 2 a _{0}^{3} + 8 a _{0} ) ^{\frac{4}{5}} - 44 a _{0} ( 6 a _{0}^{2} + 8 )}{100 ( 2 a _{0}^{3} + 8 a _{0} ) ^{\frac{4}{5}}}

y = \frac{0.44 ( 6 a _{0}^{2} + 8 )}{( 2 a _{0}^{3} + 8 a _{0} ) ^{\frac{4}{5}}} x + \frac{220 5 2 a _{0}^{3} + 8 a _{0} ( 2 a _{0}^{3} + 8 a _{0} ) ^{\frac{4}{5}} - 44 a _{0} ( 6 a _{0}^{2} + 8 )}{100 ( 2 a _{0}^{3} + 8 a _{0} ) ^{\frac{4}{5}}}

作图

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