※ 引述《alan0824 (無敵小黑猴)》之銘言：
第一題:Suppose that f(x+y)=f(x)f(y) for all x and y. Show that if f'(0) exist
than f'(a) exist and f'(a)=f(a)f'(0)
第二題:Find the equation of the tangent line to y=tanx at x=0
y'=(tanx)'=(secx)^2 將0帶入....
y'=(sec0)^2=1
第三題:y=(2x-3)/(x^2+4)^2 find Dxy
Dx(y)=Dx[(2x-3)(x^2+4)^(-2)]
=2(x^2+4)^(-2)+(-2)(2x-3)(2x)(x^2+4)^(-3)
=(-6x^2-12x+8)(x^2+4)^(-3)
第四題:G'(1) if G(t)=(t^2+9)^3*(t^2-2)^4
G'(t)=3(2t)(t^2+9)^2*(t^2-2)^4+4(2t)(t^2-2)^3*(t^2+9)^3
=2t(t^2+9)^2*(t^2-2)^3*(7t+30)
第五題:G'(1/2) if G(s)=cos拍s*sin^2拍s
G'(s)=[cosπs*(sinπs)^2]'
=-π(sinπs)(sinπs)^2+2π(sinπs)(cosπs)(cosπs)
G'(1/2)=-π[sin(π/2)]^3+2π[sin(π/2)][cos(π/2)]^2
=-π(√2/4)+2π(√2/4)
=(√2/4)π
第六題:Find d^3y/dx^3 (好像是微分三次的意思) y=sin(7x)
y'=7cos(7x)--------dy/dx
y"=-49sin(7x)------d^2y/(dx)^2
y"'=-343cos(7x)-----d^3y/(dx)^3
先降子好了...有的話我在問
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