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The functions s(x) s(x) and t(x) t(x) are differentiable. The function u(x) u(x) is defined as: u(x)=s(x)t(x) u(x)= \frac{s(x)}{t(x)} If s(6)=7 s(6)= 7 , s(6)=5 s'(6)= 5 , t(6)=9 t(6)= 9 , and t(6)=2 t'(6)= 2 , what is u(6) u'(6) ? Simplify any fractions. u(6)= u'(6)=

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Q. The functions s(x) s(x) and t(x) t(x) are differentiable. The function u(x) u(x) is defined as: u(x)=s(x)t(x) u(x)= \frac{s(x)}{t(x)} If s(6)=7 s(6)= 7 , s(6)=5 s'(6)= 5 , t(6)=9 t(6)= 9 , and t(6)=2 t'(6)= 2 , what is u(6) u'(6) ? Simplify any fractions. u(6)= u'(6)=
  1. Given Information: Write down the given information.\newlineWe are given:\newlines(6)=7s(6) = 7\newlines(6)=5s'(6) = 5\newlinet(6)=9t(6) = 9\newlinet(6)=2t'(6) = 2\newlineWe need to find u(6)u'(6) where u(x)=s(x)t(x)u(x) = \frac{s(x)}{t(x)}.
  2. Quotient Rule: Use the quotient rule to find u(x)u'(x). The quotient rule states that if u(x)=s(x)t(x)u(x) = \frac{s(x)}{t(x)}, then u(x)=s(x)t(x)s(x)t(x)(t(x))2u'(x) = \frac{s'(x)t(x) - s(x)t'(x)}{(t(x))^2}.
  3. Substitute Values: Substitute the given values into the quotient rule formula.\newlineu(6)=s(6)t(6)s(6)t(6)(t(6))2u'(6) = \frac{s'(6)t(6) - s(6)t'(6)}{(t(6))^2}\newlineu(6)=(5×97×2)(9)2u'(6) = \frac{(5 \times 9 - 7 \times 2)}{(9)^2}
  4. Perform Calculations: Perform the calculations.\newlineu(6)=451481u'(6) = \frac{45 - 14}{81}\newlineu(6)=3181u'(6) = \frac{31}{81}

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