Differentiate (x\(^2\) - \(\frac{1}{x}\))\(^2\) with respect to x
A
4x3 - 4x - 2/x
B
4x3 - 2 + 2/x3
C
4x3 - 2 - 2/x3
D
4x3 - 3x + 2/x
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
y = (x\(^2\) - \(\frac{1}{x}\))\(^2\)
y = (x\(^2\) - \(\frac{1}{x}\))(x\(^2\) - \(\frac{1}{x}\))
y = x\(^4\) - x - x + 1/x2
y = x\(^4\) - 2x + 1/x2
y = x\(^4\) - 2x + x-2
dy/dx = 4x\(^3\) - 2 - 2x\(^-3\)
= 4x\(^3\) - 2 - \(\frac{2}{x^3}\)
Source: Myschool Past Questions Archive (Record #8696)