Differentiate : X/(1 - Ln(x - 1)) | Wyzant Ask An Expert

Subject ZIP Search Search Find an Online Tutor Now Ask Ask a Question For Free Login Math Calculus Differentiate : x/(1 - ln(x - 1)) Differentiate : x/(1 - ln(x - 1)) #27, p 223 Follow • 2 Add comment More Report

1 Expert Answer

Best Newest Oldest By: Best Newest Oldest We have a choice between using the product rule or the quotient rule. I'm going to go with the product rule in this case. Remember that when we have something of the form 1/(.....), we can always rewrite it as (.....)-1. Any time something is in the denominator, we can bring it to the numerator and negate the sign of its exponent. We'll do that to get: f(x)= x(1-ln[x-1])-1 so now we're looking at x multiplied by a term in brackets. The product rule is: d/dx(g(x)*h(x))= g*h'+h*g' (using primes for derivatives). We have:

• g(x)=x
• g'(x)=1
• h(x)=(1-ln[x-1])-1
• h'(x)= (-1)*(1-ln[x-1])-2*d/dx(1-ln[x-1]) = -(1-ln[x-1])-2(-1/[x-1]) = -1/[(1-ln[x-1])2*(x-1)] (via chain rule)

Substituting into the product rule, we get the derivative to be {-x/[(1-ln[x-1])2*(x-1)]} + {1/(1-ln[x-1])} Upvote • 0 Downvote Comment • 1 More Report Report

10/22/15

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