# Thread: Can somebody help me applying the definition of derivatives to solve this?

1. ## Can somebody help me applying the definition of derivatives to solve this?

Can somebody help me applying the definition of derivatives to solve this?

1. Find the slope of the curve y = sqroot(x) when x=1
2. Find the equation of the tangent line to the curve at the given point:

y = 5/(1-3x) (2, -1)

Please remember we do not know any property of derivatives only use the definition.
thanks!!

2. Off the top of my head, doesn't the 'definition of derivatives' refer to First Principles i.e.
limit as h->0 for (f(x-h) - f(x)) / h
That doesn't assume any properties of derivatives, just the raw idea.

3. hello
1) $\displaystyle \lim_{x\to 1}\frac{f(x)-f(1)}{x-1}$
2) the equation should be of the form : $\displaystyle y = {f}'(x_{0})(x-x_{0})+f(x_{0})$

4. Originally Posted by chug1
Off the top of my head, doesn't the 'definition of derivatives' refer to First Principles i.e.
limit as h->0 for (f(x-h) - f(x)) / h
That doesn't assume any properties of derivatives, just the raw idea.

yes exact. can you solve those problems please?

5. Seems to me the more important question is "Can you solve these problems?"

6. of course yes!