The functions s(x) and t(x) are differentiable. The function u(x) is defined as: u(x)= (s(x))/(t(x)) If s(10)= 5,s^(')(10)= 3,t(10)= 2, and t^(')(10)= -4, what is u^(')(10)? Simplify any fractions. u^(')(10)= _____

Apply Quotient Rule: To find u'(x), we need to use the quotient rule for derivatives, which states that if u(x) = s(x)/t(x), then u'(x) = (s'(x)t(x) - s(x)t'(x))/(t(x))^2. We will apply this rule to find u'(10).Calculate Numerator: First, we calculate the numerator of the quotient rule: s'(10)t(10) - s(10)t'(10). Plugging in the given values, we get 3*2 - 5*(-4).Calculate Denominator: Performing the multiplication, we have 6 - (-20), which simplifies to 6 + 20.Find u'(10): Adding the numbers together, we get 26 for the numerator of the derivative at x = 10.Divide Numerator by Denominator: Next, we calculate the denominator of the quotient rule: (t(10))^2. Plugging in the given value, we get (2)^2.Simplify Fraction: Squaring the number 2, we get 4 for the denominator of the derivative at x = 10.Now, we divide the numerator by the denominator to find u'(10): 26/4.Simplifying the fraction 26/4, we get 6.5 or 13/2 as the value of u'(10).

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The functions $s(x)$ and $t(x)$ are differentiable. $\newline$ The function $u(x)$ is defined as: $u(x)= \frac{s(x)}{t(x)}$ $\newline$ If $s(10)= 5$ , $s'(10)= 3$ , $t(10)= 2$ , and $t'(10)= -4$ , what is $u'(10)$ ? $\newline$ Simplify any fractions. $\newline$ $u'(10)=$ _____

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Algebra 1

Compare linear and exponential growth

Full solution

Q. The functions

s(x)

and

t(x)

are differentiable.

\newline

The function

u(x)

is defined as:

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

\newline

s(10)= 5

s'(10)= 3

t(10)= 2

, and

t'(10)= -4

, what is

u'(10)

\newline

Simplify any fractions.

\newline

u'(10)=

_____

Apply Quotient Rule: To find $u'(x)$ , we need to use the quotient rule for derivatives, which states that if $u(x) = \frac{s(x)}{t(x)}$ , then $u'(x) = \frac{s'(x)t(x) - s(x)t'(x)}{(t(x))^2}$ . We will apply this rule to find $u'(10)$ .
Calculate Numerator: First, we calculate the numerator of the quotient rule: $s'(10)t(10) - s(10)t'(10)$ . Plugging in the given values, we get $3 \times 2 - 5 \times (-4)$ .
Calculate Denominator: Performing the multiplication, we have $6 - (-20)$ , which simplifies to $6 + 20$ .
Find $u'(10)$ : Adding the numbers together, we get $26$ for the numerator of the derivative at $x = 10$ .
Divide Numerator by Denominator: Next, we calculate the denominator of the quotient rule: $(t(10))^2$ . Plugging in the given value, we get $(2)^2$ .
Simplify Fraction: Squaring the number $2$ , we get $4$ for the denominator of the derivative at $x = 10$ .
Simplify Fraction: Squaring the number $2$ , we get $4$ for the denominator of the derivative at $x = 10$ .Now, we divide the numerator by the denominator to find $u'(10)$ : $\frac{26}{4}$ .
Simplify Fraction: Squaring the number $2$ , we get $4$ for the denominator of the derivative at $x = 10$ .Now, we divide the numerator by the denominator to find $u'(10): \frac{26}{4}$ .Simplifying the fraction $\frac{26}{4}$ , we get $6.5$ or $\frac{13}{2}$ as the value of $u'(10)$ .