Chain Rule: Prove the QuotientDate: 05/30/2001 at 09:47:45 From: David Liu Subject: Proving the quotient rule using the product and chain rule I've been asked to prove the quotient where u/v is uv^-1 using the product rule and the chain rule for (dv^-1/dx I get this far: V^-1*(du/dx)+u(dv^-1/dx) but I don't know how to use the chain rule to to find dv^-1/dx and then convert it all into the quotient rule. Could you help by giving me a step-by-step guide to the answer? Thank you! Date: 05/30/2001 at 13:06:35 From: Doctor Peterson Subject: Re: Proving the quotient rule using the product and chain rule Hi, David. You applied the product rule to u * v^-1 and got d/dx (u * v^-1) = v^-1 * du/dx + u * d(v^-1)/dx Now you have to apply the chain rule to find d(v^-1)/dx. You might find this clearer if you define a new variable w = v^-1 The chain rule says dw/dx = dw/dv * dv/dx Since dw/dv = -v^-2, this gives d(v^-1)/dx = -v^-2 * dv/dx You should be able to finish the work. If not, write back and show again how far you got. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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