Limits (The limit is shown below)

[zenith lynx]

I have to solve this in two different ways, one with limit rules and special limits and the other way is by definition of the deritative but I have literally no clue

[zenith lynx]

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[zenith lynx]

Limits (The limit is shown below)

[zenith lynx]

This is the correct one mb

[lilac arch]

,, \lim_{h \to 0} \frac{\frac{1}{(x+h)^2}-\frac{1}{x^2}}{h} = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h} =: f'(x)

[velvet zephyr]

bacc (unhelpful)

[lilac arch]

If you wanna solve this try to bring the fractions together

[zenith lynx]

okay imma try that!

any tips for the other way?

btw wouldnt it be -f(h)?

oh no mb

[zenith lynx]

ye i am stuck i cant

[lilac arch]

,, \lim_{h \to 0} \frac{\frac{1}{(x+h)^2}-\frac{1}{x^2}}{h} = \lim_{h \to 0} \frac{\frac{x^2-(x+h)^2}{x^2(x+h)^2}}{h} = \lim_{h \to 0} \frac{\frac{-2hx - h^2}{x^2(x+h)^2}}{h} = \lim_{h \to 0} \frac{-2hx - h^2}{hx^2(x+h)^2}

[lilac arch]

Now factor an h out