微積分小問題!!請各位大大幫我吧!!

Question

1. if y=tanx, find f\'\'(拍/4)
2. if (x)=6x/e的x次方+1 , find f\'(0)
3.find the derivative of f(x)=e的x次方(x的平方+2)
4.if f(X)=2e的x次方-3x22的e次方+根號 e, find f\'(x)
5.if f(x)=1/x的平方 . find f\'\'(1)

第四題題目有誤!!
4.if f(X)=2e的x次方-3x的e次方+根號 e, find f\'(x)
第2題ㄉ+1是在分母沒錯!!

Answer 1

1. f(x)=tanxf'(x)=sec²xf''(x)=2secx*secx*tanx=2sec2x*tanxf''(π/4)=2(2/√2)2*1=42.f(x)=6x/(ex+1)f'(x)=[6(ex+1)-6x(ex)]/(ex+1)2f'(0)=[6(2)-0(1)]/4=33.f (x)=ex(x²+2)f '(x)=ex(x²+2)+ex(2x)4.f(x)=2ex-3xe+√ef'(x)=2ex-3exe-15.f(x)=1/x²f'(x)=-2x/x4=-2/x3f''(x)=6x2/x6=6/x4f''(1)=6

2006-06-30 15:42:18 補充：
第二題...兩位答案不一樣
有人可以來算一下第二題嗎?

Answer 2

 1. y = f(x) = tan x f '(x) = sec2 x　f ''(x) = 2 sec x sec x tan x = 2 sec2 x tan xf ''(π/4) = 2 sec2(π/4)tan(π/4) = 2(√2)2 ‧1 = 42. f(x) = 6x / (ex + 1)f '(x) = ((ex + 1)‧6 - 6x‧ex ) / (ex + 1) = (6ex + 6 - 6xex) / (ex + 1)f '(0) = (6 + 6) / (1 + 1) = 63. f(x) = ex(x 2 + 2)f '(x) = ex(x 2 + 2) + 2xex4. f(x) = 2ex -3x22e +√ef '(x) = 2ex - 3‧22e 5. f(x) = 1/x2 f '(x) = -2/x3 f ''(x) = 6/x4 f ''(1) = 6/1 = 6抱歉如果誤解題目意思,請再說一聲,第4題最可能弄錯

2006-06-26 00:02:16 補充：
第2題的 +1 是否不在分母?

2006-06-26 11:15:13 補充：
4.f(x) = 2e^x - 3x^e + √ef '(x) = 2e^x - 3ex^(e-1)