Question

How do I find d/dx (ln((x+1)/(sqrt(x-2)))?

Answer 1

For this, need to use the product rule u'v +v'u. u being lnx+1 and v being sqrtx-2...To make this more simpler, bring v to the top out of the denominator so then it becomes (ln(x+1)*((x-2)^(-1/2). as a sqrt of a number is to the 1/2 power, and bring it from denominator makes it negative because reciprocal.Then take derivative using the product rule.

Answer 2

Thus, the answer should be (1/x+1)(x-2)^(-1/2) - 1/2(x-2)^(-3/2)