# Thread: Finding the derivative sans quotient rule

1. ## Finding the derivative sans quotient rule

Find the derivative of the following equation;

(hint: do not use the quotient rule)

x^2 - 4
-------
x^4

Is the hint a trick? I'm not sure whether this equation is even differentiable, when graphed it isn't continuous and to be differentiable an equation has to be continuous, right?

2. Originally Posted by rdryden
Find the derivative of the following equation;

(hint: do not use the quotient rule)

x^2 - 4
-------
x^4

Is the hint a trick? I'm not sure whether this equation is even differentiable, when graphed it isn't continuous and to be differentiable an equation has to be continuous, right?
It's obviously not differentiable at $x = 0$ since the function is not continuous at $x = 0$.

Divide everything by $x^4$.

So $\frac{x^2 - 4}{x^4} = x^{-2} - 4x^{-4}$.

Can you find the derivative now?