✔ 最佳答案
1.f(x): -x²+4x-9
f'(x) = -2*x^(2-1) + 4(1)x^(1-1) - 0 = 4-2x
2.f(x)= -x²+9x-2
f'(x) = -2*x^(2-1) + 9(1)x^(1-1) - 0 = 9-2x
3.f(x)= 2x³+1
f'(x) = 2*3*x(3-2) + 0 = 6x²
4.f(x)= -2x³+5
f'(x) = -2*3*x(3-2) + 0 = -6x²
5.f(x)=4+4/x = 4 + x^(-1)
f'(x) = 0 + (-1)*x^(-1-1) = -1/x²
6.f(x)= 6/x-2 = 6*x^(-1) - 2
f'(x) = 6*(-1)*x^(-1-1) - 0 = -6/x²
7.f(x)=5+3√x = 5 + 3*x^(1/2)
f'(x) = 0 + (1/2)*3*x^(1/2 - 1) = (3/2)*x^(-1/2) = 3/2√x
8.f(x)=3-7√x = 3 - 7*x^(1/2)
f'(x) = 0 - (1/2)*7*x^(1/2 - 1) = (-7/2)*x^(-1/2) = -7/2√x
補充:
當f(x)=任意常數,則f'(x)=0。
當f(x)=x^n,其中n為有理數,則f'(x)=nx^(n-1)。
如果在問題方面的表達有所誤解,例如6/x - 2 或6/(x-2),請告知,以便修正。
2009-07-31 17:30:56 補充:
第5題修正:
5.f(x)=4+4/x = 4 + 4*x^(-1)
f'(x) = 0 + 4*(-1)*x^(-1-1) = -4/x²
2009-07-31 19:50:23 補充:
第五題修正:
5.f(x)=4+4/x = 4 + 4x^(-1)
f'(x) = 0 + 4(-1)*x^(-1-1) = -4/x²