What is the derivative wrt to x of...?

Question

y=f(x)/g(x)

hint: use product rule

please answer.

Thanks

Answer 1

You are being asked to derive the quotient rule. This and other derivative rules can be found at: http://www.mathwords.com/d/derivative_ru...

Here is how to do it:

y=f(x)/g(x) {I am going to remove the (x) for simplicity}

y=f/g = f (1/g) = f(g^-1) now by the product rule:

if y = f(g^-1) then y' = f'(g^-1) + f(-1)(g^-2)(g') = f '/ g - (f g') / (g^2)

now multiply the first term by g/g to get a common denominator for:

y ' = (f ' g) / g^2 - (f g') / g^2 = (f 'g - f g' ) / g^2

This is the standard form for the derivative of a quotient.

Hope this helps!