Math Function, pls kindly help~

2008-02-22 4:54 pm
a) Given f(x) = 7x^2 / (x-1), determine f'"(x)
b) Given x^2y + y^3 = 2, determine y".

Thank You

回答 (1)

2008-02-22 6:07 pm
✔ 最佳答案
a) f(x) = 7x² / (x-1)

f'(x) = ((x-1)(14x) - (7x²)(1)) / (x-1)²
= (14x²-14x-7x²) / (x-1)²
= (7x²-14x) / (x-1)²
= 7x(x-2) / (x²-2x+1)

f''(x) = ((x-1)²(14x-14) - 7x(x-2)(2x-2)) / (x-1)^4
=(14(x-1)³ - 14x(x-2)(x-1)) / (x-1)^4
=14((x-1)² - x(x-2)) / (x-1)³
=14(x²-2x+1-x²+2x) / (x-1)²
=14 / (x-1)²

b) x²y + y³ = 2 ???

Or x^(2y) + y³ = 2 ??


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