## anonymous 3 years ago Find the derivative of the given function at the indicated point. f(x)=1/x,a = 2 f′(a)= lim (f(a+h) - f(a))/h h --> 0

1. anonymous

Could you show steps please, im really confused.

2. campbell_st

rewrite your function in index form $f(x) = x^{-1}$ can you differentiate the function..?

3. across

You have that $$f(x)=1/x$$ and are asked to compute its derivative at $$a=2$$. Then$f'(a)=\lim_{h\to0}\frac{1/(2+h)-1/2}{h}.$Can you simplify this and compute its limit?

4. anonymous

Thanks for getting me started across. Ill see if I can simplify.

5. campbell_st

oops 1st principles $\lim_{h \rightarrow0} \frac{ \frac{1}{x + h} - \frac{1}{h}}{h}$ put the fractions in the numerator over a common denominator $\lim_{h \rightarrow 0} \frac{\frac{x - (x +h)}{x(x+h)}}{h}$ so it can then be simplified to $\lim_{h \rightarrow 0} \frac{\frac{-h}{x(x + h)}}{h}$ or $\lim_{h \rightarrow 0} \frac{-h}{hx(x + h)}$ cancel the common factor and then substitute h = 0 to get the derivative

6. anonymous

Oh I see, would it also simplify further to 1/x^2. Also at a=2, the deravitive of f(x) = 1/4 right?

7. campbell_st

well it simplifies to -1/x^2

8. campbell_st

so you need to check you value for a = 2

9. anonymous

Oh, careless mistake. Thank you so much, this really helped.