How to solve derivative/limit of f ( x ) = x 4 − x 2

Question

How to solve derivative/limit of    f  (  x  )  =  x      4    −          x      2

nuvolor8 · Accepted Answer

I think your algebra could look more like:

\begin{aligned} \frac{(x + h) \sqrt{4 - (x + h)^{2}} - x \sqrt{4 - x^{2}}}{h} \cdot \frac{(x + h) \sqrt{4 - (x + h)^{2}} + x \sqrt{4 - x^{2}}}{(x + h) \sqrt{4 - (x + h)^{2}} + x \sqrt{4 - x^{2}}} \\ = \frac{(x + h)^{2} (4 - (x + h)^{2}) - x^{2} (4 - x^{2})}{h ((x + h) \sqrt{4 - (x + h)^{2}} + x \sqrt{4 - x^{2}})} \end{aligned}

This leaves no radicals in the numerator.
In the numerator, once this is multiplied out, all h-free terms will have canceled out through adding terms to their negatives.
Then you can factor h from the top and cancel the h in the denominator. Then it will be OK to just let

h \to 0

How to solve derivative/limit of f ( x ) = x <msqrt> 4 −

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