Question

在线急 详细解答过程：求函数在指定点处的导数值

求函数在指定点处的导数值 f(t)=（t+sint ）分之（t-sint ）在 t =2分之pai处的导数值

求详细解答过程啊~~~O(∩_∩)O谢谢

参考答案：dx分之dy|(t=2分之π) = —1
sorry 更正一下参考答案是：【（pai+2）^2】分之8

Answer 1

你给的参考答案好像不对吧

追问

sorry 更正一下参考答案是：【（pai+2）^2】分之8

sorry 更正一下参考答案是：【（pai+2）^2】分之8

Answer 2

f(t)'=[(t-sint)'(t+sint)-(t-sint)(t+sint)']/(t+sint)^2
=[(1-cost)(t+sint)-(t-sint)(1+cos)]/(t+sint)^2

Answer 3

f(t)=(t-sint)/(t+sint)
f'(t)=[(1-cost)(t+sint)-(t-sint)(1+cost)]/(t+sint)^2
f'(π/2)=[π/2+1-(π/2-1)]/(π/2+1)^2=2/(π/2+1)^2

Answer 4

Differentiate the function with respect to t using chain rule and then substitute value of t into the fisrt degree of the differentiation of the function.