微分一題

[ruby0519]

老師請問一題微分
x=t
y=根號t
t=1/4
求d^2y/dx^2=
謝謝您

[thepiano]

y = √t = √x
y' = (1/2)x^(-1/2)
y'' = (-1/4)x^(-3/2)
y''(1/4) = (-1/4)(1/4)^(-3/2) = -2

[ruby0519]

謝謝老師

[ruby0519]

請問老師是轉換成t微分兩次嗎
可以請教微分的過程嗎?

[thepiano]

之前誤解題意，已修正如上

[ruby0519]

y''(1/4) = (-1/4)(1/4)^(-3/2) = -2
老師您y''後面多寫了(1/4)對不對

[thepiano]

沒有多寫，那是用 1/4 代入的意思