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受欢迎的微积分 >

tangent ((a+h)^4)/h

解答

切线

\frac{( a + h ) ^{4}}{h}

解答

y = \frac{3 a _{1}^{4} + 8 a a _{1}^{3} + 6 a ^{2} a _{1}^{2} - a ^{4}}{a _{1}^{2}} h + \frac{2 a ^{4} + 4 a ^{3} a _{1} - 4 a a _{1}^{3} - 2 a _{1}^{4}}{a _{1}}

求解步骤

计算在一般点

h = a_{1}

的切线

找到切点:

(a_{1}, \frac{( a + a _{1} ) ^{4}}{a _{1}})

计算

y = \frac{( a + h ) ^{4}}{h}

的斜率:

\frac{d y}{d h} = \frac{4 h ( a + h ) ^{3} - ( a + h ) ^{4}}{h ^{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{3 a _{1}^{4} + 8 a a _{1}^{3} + 6 a ^{2} a _{1}^{2} - a ^{4}}{a _{1}^{2}}

找到斜率 m=

\frac{3 a _{1}^{4} + 8 a a _{1}^{3} + 6 a ^{2} a _{1}^{2} - a ^{4}}{a _{1}^{2}}

且穿过

(a_{1}, \frac{( a + a _{1} ) ^{4}}{a _{1}})

的直线:

y = \frac{3 a _{1}^{4} + 8 a a _{1}^{3} + 6 a ^{2} a _{1}^{2} - a ^{4}}{a _{1}^{2}} h + \frac{2 a ^{4} + 4 a ^{3} a _{1} - 4 a a _{1}^{3} - 2 a _{1}^{4}}{a _{1}}

y = \frac{3 a _{1}^{4} + 8 a a _{1}^{3} + 6 a ^{2} a _{1}^{2} - a ^{4}}{a _{1}^{2}} h + \frac{2 a ^{4} + 4 a ^{3} a _{1} - 4 a a _{1}^{3} - 2 a _{1}^{4}}{a _{1}}

作图

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