Question

find f ' (a)
f(x)=x^-2

Answer 1

f(a+h) - f(a) / h = (a+h)^-2 - a^-2 / h = ( 1/(a+h)^2 - 1/a^2 ) / h

= a^2 - (a^2 + 2ah + h^2)
---------------------
h(a^2+2ah+h^2)(a^2)

Answer 2

f(a+h) - f(a) / h = (a+h)^-2 - a^-2 / h = ( 1/(a+h)^2 - 1/a^2 ) / h

= a^2 - (a^2 + 2ah + h^2)
---------------------
h(a^2+2ah+h^2)(a^2)

Answer 3

just not sure where to go from here

Answer 4

expand the bracket in the numerator

Answer 5

the a^2 terms will cancel out in the numerator

Answer 6

then factorise the numerator and you should find and 'h' can cancel between numerator and denominator

Answer 7

finally take the limit as h tends to zero - which in this case you can just set h=0

Answer 8

i got

-2a
---
a^4

Answer 9

that is correct - now simplify this

Answer 10

-2/a^3

Answer 11

perfect! :)

Answer 12

thanks!!!!

Answer 13

yw :)