How do you find f'(x) using the definition of a derivative for #f(x)=(1-6t)/(5+t)#?

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How do you find f'(x) using the definition of a derivative for #f(x)=(1-6t)/(5+t)#?

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Answer 1 · 2015-09-23T20:25:29

#-31/(5+t)^2#

Explanation:

#f(t)=(1-6t)/(5+t)#
#f(t+h)=(1+6(t+h))/(5+(t+h))#
#f(t+h)-f(t)=(1-6(t+h))/(5+(t+h))-(1-6t)/(5+t)=(5+t-6(t^2+5h+5t+ht)-5-t-h+30t+6t^2+6ht)/((5+t+h)(5+t))=(-31h)/((5+t+h)(5+t))#
#Lt_(h->0)((f(t+h)-f(h))/h)=Lt_(h->0)(-31h)/(h(5+t+h)(5+t))=Lt_(h->0)(-31)/((5+t+h)(5+t))=-31/(5+t)^2#

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How do you find f'(x) using the definition of a derivative for #f(x)=(1-6t)/(5+t)#?

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