Posted by Sckricks on Thursday, October 17, 2013 at 12:27pm.
If f'(x) = 2xln(4(x^22.75))+(2x^3)/(x^22.75) find the domain.

Calculus  Reiny, Thursday, October 17, 2013 at 12:37pm
remember we can only take logs (or ln) of positive numbers, so
4(x^2  2.75) > 0 also for 2x^3/(x^2  2.75), the denominator cannot be zero
But we already included that in our first restriction
4(x^2  2.75) > 0
x^2  2.75 < 0
x^2 < 2.75  > x^2 < 11/4
 √11/2 < x < √11/2

Calculus  Steve, Thursday, October 17, 2013 at 12:40pm
since ln(x) has domain x>0, we need
4(x^22.75) > 0
√11/2 < x < √11/2
Note that this also works for the 2nd term, since it must be nonzero. That is,
x ≠ √11/2
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