Find the derivative of the following, can anybody help me? 3 questions?

2011-02-15 10:37 am
1)

5x^4 + 2x - 1

2)

2sqrt(x) - 3/x + 12

3)

3x^2 - 7x^3 / x^2 < -------------- (x not equal to zero)

i need full working steps and even better with explanations

回答 (2)

2011-02-15 2:14 pm
✔ 最佳答案
Qu 1
f `(x) = 20 x ³ + 2

Qu 2
f (x) = 2 x^(1/2) - 3/x + 12
f `(x) = x^(-1/2) + 3/x ² = 1/x^(1/2) + 3/x ²

Qu 3
Presentation is unclear and will assume that :-
f (x) = ( 3 x ² - 7 x ³ ) / x ²
f (x) = 3 - 7x
f `(x) = - 7
2011-02-15 6:55 pm
derivative of x^m = m x^(m-1) and derivative of a constant is zero, i.e. d/dx of 10 = d/dx of 10* x^0 = 0
1. derivative of 5 x^4 + 2x -1 = 5* 4x*3 + 2 = 20 x^3 +2
2. derivative of 2 sqrt(x) -3/x +12 or 2 x^0.5 - 3 x^-1 +12 is
2* 0.5 x^-0.5 - 3*(-1) x^-2 + 0
x^-0.5 + 3 x^-2
1/sqrt(x) + 3/x^2
3 derivative of 3x^2 - 7x^3/x^2 or 3x^2 - 7x^(3-2) or 3x^2 - 7x is
3*2x - 7=6x-7


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