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

Given Information: Write down the given information. We are given: s(6) = 7 s'(6) = 5 t(6) = 9 t'(6) = 2 We need to find u'(6) where u(x) = s(x)/t(x).Quotient Rule: Use the quotient rule to find u'(x). The quotient rule states that if u(x) = s(x)/t(x), then u'(x) = (s'(x)t(x) - s(x)t'(x))/(t(x))^2.Substitute Values: Substitute the given values into the quotient rule formula. u'(6) = (s'(6)t(6) - s(6)t'(6))/(t(6))^2 u'(6) = (5 * 9 - 7 * 2)/(9)^2Perform Calculations: Perform the calculations. u'(6) = (45 - 14)/(81) u'(6) = 31/81

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

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Algebra 2

Find the vertex of the transformed function

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Q. The functions

s(x)

and

t(x)

are differentiable. The function

u(x)

is defined as:

u(x)= \frac{s(x)}{t(x)}

s(6)= 7

s'(6)= 5

t(6)= 9

, and

t'(6)= 2

, what is

u'(6)

? Simplify any fractions.

u'(6)=

Given Information: Write down the given information. $\newline$ We are given: $\newline$ $s(6) = 7$ $\newline$ $s'(6) = 5$ $\newline$ $t(6) = 9$ $\newline$ $t'(6) = 2$ $\newline$ We need to find $u'(6)$ where $u(x) = \frac{s(x)}{t(x)}$ .
Quotient Rule: Use the quotient rule to find $u'(x)$ . The quotient rule states that if $u(x) = \frac{s(x)}{t(x)}$ , then $u'(x) = \frac{s'(x)t(x) - s(x)t'(x)}{(t(x))^2}$ .
Substitute Values: Substitute the given values into the quotient rule formula. $\newline$ $u'(6) = \frac{s'(6)t(6) - s(6)t'(6)}{(t(6))^2}$ $\newline$ $u'(6) = \frac{(5 \times 9 - 7 \times 2)}{(9)^2}$
Perform Calculations: Perform the calculations. $\newline$ $u'(6) = \frac{45 - 14}{81}$ $\newline$ $u'(6) = \frac{31}{81}$