3. If u = (x2+9)1/2 and v = 3x2-2x, then what is du/dv as a function of x?
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A. 1/(4(3x-1)(x2+9)1/2) for x ¹ 1/3 |
B. (3x-1)/(2(x2+9)1/2) |
C. (2x(3x-1))/(x2+9)1/2 |
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D. x/(2(3x-1)(x2+9)1/2) for x ¹ 1/3 |
Solution: The answer is D
First find du, by taking the derivative of u with respect to x.
Multiply both sides by dx so that,
Similarly, find dv.
Thus, dividing du by dv. yields,
