How do you use the definition of a derivative to find the derivative of #1/x^2#?
1 Answer
Jan 29, 2016
# -2/x^3 #
Explanation:
# f'(x) = lim_(h→ 0 )( f(x+h) - f(x))/h #
# = lim_(h→0) ( 1/(x+h)^2 -1/x^2)/h #
# = lim_(h→0)( (x^2 - (x+h)^2)/(x^2(x+h)^2))/h #
# = lim_(h→0)(( x^2 - x^2 - 2hx - h^2)/(x^2(x+h)^2))/h #
# = lim_(h→0) (( -h(2x+ h))/(x^2(x+h)^2))/h#
# = lim_(h→0) 1/cancel(h) (- cancel(h) (2x+h))/(x^2(x+h)^2) #
# =( - 2x)/x^4 = -2/x^3 #
