Question

C C hen

請問這題要怎麼算

已知函數 f滿足以下條件:
f(2) = 9, f'(2) = -3, f(1) = 1,
若將函數 F 定義為 F(x) = f(x²), 則 F'(1) =
4
x
正確答案是:8.00
f' (1) = 4.

Answer 1

✨ 最佳解答 ✨

呵

F'(x)=f'(x²)=(d/dx)(f(x²))=(d/dx²)(dx²/dx)(f(x²))
=[(d/dx²)(f(x²))] [(d/dx)(x²)]
=f'(x²)2x
x=1代入，所求=f'(1²)×2×1=4×2=8

C C hen

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呵

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