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受欢迎的微积分 >

tangent y=((x^2))/(8+sqrt(x))

解答

切线

y = \frac{( x ^{2} )}{8 + x}

解答

y = \frac{4 a _{0} ( 8 + a _{0} ) - a _{0}^{\frac{3}{2}}}{2 ( 8 + a _{0} ) ^{2}} x - \frac{a _{0}^{2} ( a _{0} + 16 )}{2 ( a _{0} + 8 ) ^{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}^{2} ( 8 - a _{0} )}{64 - a _{0}})

计算

y = \frac{x ^{2}}{8 + x}

的斜率:

\frac{d y}{d x} = \frac{4 x ( 8 + x ) - x ^{\frac{3}{2}}}{2 ( 8 + x ) ^{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{4 a _{0} ( 8 + a _{0} ) - a _{0}^{\frac{3}{2}}}{2 ( 8 + a _{0} ) ^{2}}

找到斜率 m=

\frac{4 a _{0} ( 8 + a _{0} ) - a _{0}^{\frac{3}{2}}}{2 ( 8 + a _{0} ) ^{2}}

且穿过

(a_{0}, \frac{a _{0}^{2} ( 8 - a _{0} )}{64 - a _{0}})

的直线:

y = \frac{4 a _{0} ( 8 + a _{0} ) - a _{0}^{\frac{3}{2}}}{2 ( 8 + a _{0} ) ^{2}} x - \frac{a _{0}^{2} ( a _{0} + 16 )}{2 ( a _{0} + 8 ) ^{2}}

y = \frac{4 a _{0} ( 8 + a _{0} ) - a _{0}^{\frac{3}{2}}}{2 ( 8 + a _{0} ) ^{2}} x - \frac{a _{0}^{2} ( a _{0} + 16 )}{2 ( a _{0} + 8 ) ^{2}}

作图

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