The functions p(x) and q(x) are differentiable. The function v(x) is defined as: v(x)= (p(x))/(q(x)) If p(8)= 4,p^(')(8)= 2,q(8)= 3, and q^(')(8)= -1, what is v^(')(8)? Simplify any fractions. v^(')(8)=

Identify the rule: Identify the rule for differentiating a quotient. The quotient rule for differentiation states that if v(x) = p(x)/q(x), then v'(x) = (p'(x)q(x) - p(x)q'(x))/(q(x))^2.Apply the quotient rule: Apply the quotient rule using the given values. We have p(8) = 4, p'(8) = 2, q(8) = 3, and q'(8) = -1. Plugging these into the quotient rule, we get: v'(8) = (p'(8)q(8) - p(8)q'(8))/(q(8))^2 v'(8) = (2*3 - 4*(-1))/(3)^2Perform the calculations: Perform the calculations. v'(8) = (6 + 4)/(3)^2 v'(8) = 10/9

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The functions $p(x)$ and $q(x)$ are differentiable. The function $v(x)$ is defined as: $v(x)= \frac{p(x)}{q(x)}$ If $p(8)= 4$ , $p'(8)= 2$ , $q(8)= 3$ , and $q'(8)= -1$ , what is $v'(8)$ ? Simplify any fractions. $v'(8)=$

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Algebra 1

Compare linear and exponential growth

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Q. The functions

p(x)

and

q(x)

are differentiable. The function

v(x)

is defined as:

v(x)= \frac{p(x)}{q(x)}

p(8)= 4

p'(8)= 2

q(8)= 3

, and

q'(8)= -1

, what is

v'(8)

? Simplify any fractions.

v'(8)=

Identify the rule: Identify the rule for differentiating a quotient. $\newline$ The quotient rule for differentiation states that if $v(x) = \frac{p(x)}{q(x)}$ , then $v'(x) = \frac{p'(x)q(x) - p(x)q'(x)}{(q(x))^2}$ .
Apply the quotient rule: Apply the quotient rule using the given values. $\newline$ We have $p(8) = 4$ , $p'(8) = 2$ , $q(8) = 3$ , and $q'(8) = -1$ . Plugging these into the quotient rule, we get: $\newline$ $v'(8) = \frac{p'(8)q(8) - p(8)q'(8)}{(q(8))^2}$ $\newline$ $v'(8) = \frac{2 \cdot 3 - 4 \cdot (-1)}{3^2}$
Perform the calculations: Perform the calculations. $\newline$ $v'(8) = \frac{6 + 4}{3^2}$ $\newline$ $v'(8) = \frac{10}{9}$