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Quotient Rule Proof – Calculus

by Batool Akmal
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    So after proving chain rule and product rule, this should be fairly easier so we're now going to look at the proof for the quotient rule. In order to do this we are going to use the product rule because it's a bit more simpler and we're just going to apply the product rule and hopefully derive the same result that we have for the quotient rule. So let?s start to look at our proof for the quotient rule. So we're trying to prove the derivative of f of x over g of x and we're trying to prove that the derivative does actually give us the quotient rule. So this is what we are trying to do. We can rewrite this and bring the g up. So remember the g of x has a power of one, so we can bring that up and we can rewrite this as d/dx, f of x, multiplied by g of x to the minus one. So all I've done is I have brought g of x up and changed its power because it was plus one at the bottom, it now becomes a minus one. Okay so we're trying to differentiate a function, so we're trying to differentiate this but also observe this closely. This is a product of two functions so in order to differentiate it we can use the product rule. Remember what the product rule stated so the product rule said, if we just write by here, dy/dx you can do this in any order that you want but you can do it as uv dash plus vu dash so leave one as it is, differentiate the other and differenti-- leave the other second one as it is and differentiate the first. So if we start with just differentiating...

    About the Lecture

    The lecture Quotient Rule Proof – Calculus by Batool Akmal is from the course Quotient Rule, Chain Rule and Product Rule.


    Author of lecture Quotient Rule Proof – Calculus

     Batool Akmal

    Batool Akmal


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