Limit Definition of the Derivative questions

[super_chris12435]

Hi,

I'm new here and am preparing for a final exam. I'm having trouble understanding these two limit definition of a derivative questions:

Find the first derivative of the following functions using the Limit definition of the derivative

a) 5/(1-3x)^2

b) 3/sqrt(1-x)

I understand how to use the quotient and chain rules to prove, it's just the limit definition I'm not sure how to solve.

Thanks

 

[Ishuda]

The limit definition is to go back to the original definition. For example suppose we want the derivative of (f(x)=x² by the limit definition. Then we have
$\displaystyle f'(x) = lim_{h\to0} \frac{f(x+h) - f(x)}{h} = lim_{h\to0}\frac{(x+h)^2 - x^2}{h} = lim_{h\to0}\frac{h (2x + h)}{h} = lim_{h\to0} (2x + h) = 2x$

So just plug in your f(x) and slog through the algebra.