The functions u(x) and v(x) are differentiable. The function w(x) is defined as: w(x)= (u(x))/(v(x)) If u(5)= 3,u^(')(5)= -2,v(5)= 7, and v^(')(5)= 1, what is w^(')(5)? Simplify any fractions. w^(')(5)= _____

Identify the rule: Identify the rule for differentiating a quotient. The quotient rule for differentiation states that if w(x) = u(x)/v(x), then w'(x) = (v(x)u'(x) - u(x)v'(x))/(v(x))^2.Apply the quotient rule: Apply the quotient rule using the given values. We have u(5) = 3, u'(5) = -2, v(5) = 7, and v'(5) = 1. Using the quotient rule, we get: w'(5) = (v(5)u'(5) - u(5)v'(5))/(v(5))^2 w'(5) = (7 * (-2) - 3 * 1)/(7)^2Perform the calculations: Perform the calculations. w'(5) = (-14 - 3)/(49) w'(5) = (-17)/(49)

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The functions $u(x)$ and $v(x)$ are differentiable. $\newline$ The function $w(x)$ is defined as: $w(x)= \frac{u(x)}{v(x)}$ $\newline$ If $u(5)= 3$ , $u'(5)= -2$ , $v(5)= 7$ , and $v'(5)= 1$ , what is $w'(5)$ ? $\newline$ Simplify any fractions. $\newline$ $w'(5)=$ _____

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Algebra 1

Compare linear and exponential growth

Full solution

Q. The functions

u(x)

and

v(x)

are differentiable.

\newline

The function

w(x)

is defined as:

w(x)= \frac{u(x)}{v(x)}

\newline

u(5)= 3

u'(5)= -2

v(5)= 7

, and

v'(5)= 1

, what is

w'(5)

\newline

Simplify any fractions.

\newline

w'(5)=

_____

Identify the rule: Identify the rule for differentiating a quotient. $\newline$ The quotient rule for differentiation states that if $w(x) = \frac{u(x)}{v(x)}$ , then $w'(x) = \frac{v(x)u'(x) - u(x)v'(x)}{(v(x))^2}$ .
Apply the quotient rule: Apply the quotient rule using the given values. $\newline$ We have $u(5) = 3$ , $u'(5) = -2$ , $v(5) = 7$ , and $v'(5) = 1$ . Using the quotient rule, we get: $\newline$ $w'(5) = \frac{v(5)u'(5) - u(5)v'(5)}{(v(5))^2}$ $\newline$ $w'(5) = \frac{7 \cdot (-2) - 3 \cdot 1}{7^2}$
Perform the calculations: Perform the calculations. $\newline$ $w'(5) = \frac{{-14 - 3}}{{49}}$ $\newline$ $w'(5) = \frac{{-17}}{{49}}$