Find the 1st and 2nd derivatives? #(t^2-1)/(t^2+t-2#

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Answer 1 · 2017-11-09T01:48:37

#f'(t) = 1/(t+2)^2#
#f''(t) = -2/(t+2)^3#

#f(t) = (t^2-1)/(t^2+t-2)#

#= (t^2-1)/((t+2)(t-1))#

#= ((t+1)(t-1))/((t+2)(t-1))#

#= ((t+1)cancel((t-1)))/((t+2)cancel((t-1)))# [#t!=1#]

#f'(t) = ((t+2)*1 - (t+1)*1)/ (t+2)^2#

#= (t+2-t-1)/(t+2)^2#

# = 1/(t+2)^2#

#f'(t) =(t+2)^-2#

Apply power and chain rules.

#f''(t) = -2(t+2)^-3 * 1#

#= -2/(t+2)^3#