Derivative of h(x) = (f(x)g(x))/(f(x) + g(x))

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Derivative of h(x) = (f(x)g(x))/(f(x) + g(x)). This is a calculus problem where we find the derivative. We use both the quotient and the product rule for derivatives.

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too much work. this should be oneliner. just take the inverse of the initial equation 1/h = 1/g + 1/f and apply the derivative. By stipulating '-' sign one obtains h'/h^2 = f'/f^2 + g'/g^2. Then, if you like you can replace h in there by inserting the original expression.

edal

One of the best channels for explaining tricky concepts in math, this is the man!

mitrikoudsi

Hey MathSorcerer! Just found your channel through your book videos, I love the rare finds and the ideas for my own collection.

This problem was waay too basic for you man, it would've been cool to see you overview a quirky proof of a well known theorem for instance (in a book you found perhaps), or give your opinion on a big result of a theorem in one of your books. You could be the niche channel which is a step up in difficulty from the usual numberphile/3Blue1Brown etc. Anyways great videos keep up the good work.

W.M.-

what could also work is working with ln(h)=ln(f)+ln(g) - ln(f+g)
h'/h= f'/f + g'/g - (f'+g')/(f+g)
so h' = [f'/f + g'/g - (f'+g')/(f+g)] * h
Where h = fg/(f+g)

vpambspt

These clips videos re helpful sir, thanks

jamesjohn

Do you guys know any tricks for dividing 100 by a number>100 in your head? For example: 100/196

Hursimear

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