The functions f(x) and g(x) are differentiable. The function h(x) is defined as: h(x)= (f(x))/(g(x)) If f(9)= 6,f^(')(9)= 4,g(9)= 2, and g^(')(9)= -3, what is h^(')(9)? Simplify any fractions. h^(')(9)=

Given function and derivative: We are given the function h(x) = f(x)/g(x) and we need to find the derivative of h at x = 9, which is h'(9). To do this, we will use the quotient rule for derivatives, which states that if h(x) = f(x)/g(x), then h'(x) = (g(x)f'(x) - f(x)g'(x)) / (g(x))^2.Applying the quotient rule: We are given f(9) = 6, f'(9) = 4, g(9) = 2, and g'(9) = -3. Let's plug these values into the quotient rule formula to find h'(9). h'(9) = (g(9)f'(9) - f(9)g'(9)) / (g(9))^2 h'(9) = (2 * 4 - 6 * -3) / (2)^2Plugging in values: Now we perform the calculations: h'(9) = (8 + 18) / 4 h'(9) = 26 / 4 h'(9) = 6.5

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The functions $f(x)$ and $g(x)$ are differentiable. The function $h(x)$ is defined as: $h(x)= \frac{f(x)}{g(x)}$ If $f(9)= 6$ , $f'(9)= 4$ , $g(9)= 2$ , and $g'(9)= -3$ , what is $h'(9)$ ? Simplify any fractions. $h'(9)=$

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Q. The functions

f(x)

and

g(x)

are differentiable. The function

h(x)

is defined as:

h(x)= \frac{f(x)}{g(x)}

f(9)= 6

f'(9)= 4

g(9)= 2

, and

g'(9)= -3

, what is

h'(9)

? Simplify any fractions.

h'(9)=

Given function and derivative: We are given the function $h(x) = \frac{f(x)}{g(x)}$ and we need to find the derivative of $h$ at $x = 9$ , which is $h'(9)$ . To do this, we will use the quotient rule for derivatives, which states that if $h(x) = \frac{f(x)}{g(x)}$ , then $h'(x) = \frac{g(x)f'(x) - f(x)g'(x)}{(g(x))^2}$ .
Applying the quotient rule: We are given $f(9) = 6$ , $f'(9) = 4$ , $g(9) = 2$ , and $g'(9) = -3$ . Let's plug these values into the quotient rule formula to find $h'(9)$ . $\newline$ $h'(9) = \frac{g(9)f'(9) - f(9)g'(9)}{(g(9))^2}$ $\newline$ $h'(9) = \frac{2 \cdot 4 - 6 \cdot (-3)}{(2)^2}$
Plugging in values: Now we perform the calculations: $\newline$ h'( $9$ ) = $\frac{8 + 18}{4}$ $\newline$ h'( $9$ ) = $\frac{26}{4}$ $\newline$ h'( $9$ ) = $6.5$