differentiate each of the foolwing functiongs with respect to x.
1.y=x^3/3 - 3/x^3
2.y=1/x + 2/x^2 + 3/x^3
a maths.differentiate
2008-01-18 3:31 am
回答 (2)
2008-01-18 4:05 am
✔ 最佳答案
1) y = (1/3)(x^3) - 3x^(-3)dy/dx = (1/3)(3x^2)-3(-3)(x^-4)
= x^2 + 9 / x^4
2) y=1/x + 2/x^2 + 3/x^3
y = x^(-1) + 2x^(-2) + 3x^(-3)
dy/dx = -x^(-2) + 2(-2)(x^-3) + 3(-3)(x^-4)
= -1 / x^2 - 4 / x^3 - 9 / x^4
2008-01-17 20:41:06 補充：
You may also use negative indices to express your answers, i.e.( 1 ) x^2 + 9x^(-4)( 2 ) -x^(-2) - 4x^(-3) - 9x^(-4)
參考: My Maths Knowledge
2008-01-18 4:06 am
y=x^3/3 - 3/x^3
dy/dx = 3(x^2)/3 - 3x^(-3-1)(-3)
= x^2 + 9x^(-4)
y=1/x + 2/x^2 + 3/x^3
dy/dx = (-1)x^(-1-1) + 2(-2)x^(-2-1) + 3(-3)x^(-3-1)
= -x^(-2) -4x^(-3) - 9x^(-4)
dy/dx = 3(x^2)/3 - 3x^(-3-1)(-3)
= x^2 + 9x^(-4)
y=1/x + 2/x^2 + 3/x^3
dy/dx = (-1)x^(-1-1) + 2(-2)x^(-2-1) + 3(-3)x^(-3-1)
= -x^(-2) -4x^(-3) - 9x^(-4)
參考: ME~
收錄日期: 2021-04-13 14:58:59
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