Re: [微分] 有些題目不會寫!!....
※ 引述《victor7935 (victor)》之銘言：
: 1.
: Set f(x)= cosx. Show that finding f'(0) from the definition of
: derivative amounts to finding
: cosx - 1
: lim ----------
: x→0 x
f'(0) = f'(x)
x代0
f(x) - f(0)
= lim ---------------
x→0 x - 0
cosx - 1
= lim ----------
x→0 x
所以找f'(0)等同找這個極限(=0)
: 2. 2
: d [ 2 d ]
: ---- [ t ---- (t cos3t) ]
: [ ] .....這樣寫不知道看不看得懂!!= =...
: dt [ 2 ]
: dt
(tcos3t)' = cos3t - 3tsin3t
(tcos3t)'' = -3sin3t - 3sin3t - 9tcos3t
= -6sin3t -9tcos3t
(tcos3t)''' = -18cos3t - 9cos3t + 27tsin3t
= -27cos3t + 27tsin3t
所以原式 = [t^2 (tcos3t)'']'
= 2t (tcos3t)'' + t^2 (tcos3t)'''
(tcos3t)''和 (tcos3t)''' 都已經求出來了
代入上式就好
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