Let g be a function such that g(5)=7 and g^(')(5)=-2. Let h be the function h(x)=x. Evaluate (d)/(dx)[g(x)*h(x)] at x=5.

Apply Product Rule: Use the product rule for differentiation: (f * g)' = f' * g + f * g'.Differentiate Functions: Differentiate g(x) to get g'(x) and h(x) to get h'(x). Since h(x) = x, h'(x) = 1.Evaluate Derivatives: Evaluate g'(5) and h(5) using the given information. g'(5) = -2 and h(5) = 5.Apply Product Rule Formula: Plug the values into the product rule formula. (d)/(dx)[g(x)*h(x)] at x=5 = g'(5) * h(5) + g(5) * h'(5).Substitute Values: Substitute the known values into the equation. (d)/(dx)[g(x)*h(x)] at x=5 = (-2) * 5 + 7 * 1.Perform Multiplication: Perform the multiplication. (d)/(dx)[g(x)*h(x)] at x=5 = -10 + 7.Add Results: Add the results to get the final answer. (d)/(dx)[g(x)*h(x)] at x=5 = -3.

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Let
g be a function such that
g(5)=7 and
g^(')(5)=-2.
Let
h be the function
h(x)=x.

Evaluate
(d)/(dx)[g(x)*h(x)] at
x=5.

- Let $g$ be a function such that $g(5)=7$ and $g^{\prime}(5)=-2$ . $\newline$ - Let $h$ be the function $h(x)=x$ . $\newline$ Evaluate $\frac{d}{d x}[g(x) \cdot h(x)]$ at $x=5$ .

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Q. - Let

g

be a function such that

g(5)=7

and

g^{\prime}(5)=-2

\newline

- Let

h

be the function

h(x)=x

\newline

Evaluate

\frac{d}{d x}[g(x) \cdot h(x)]

x=5

Apply Product Rule: Use the product rule for differentiation: $f * g$ ' = f' * g + f * g'.
Differentiate Functions: Differentiate $g(x)$ to get $g'(x)$ and $h(x)$ to get $h'(x)$ . $\newline$ Since $h(x) = x$ , $h'(x) = 1$ .
Evaluate Derivatives: Evaluate $g'(5)$ and $h(5)$ using the given information. $\newline$ $g'(5) = -2$ and $h(5) = 5$ .
Apply Product Rule Formula: Plug the values into the product rule formula. $\newline$ $(\frac{d}{dx})[g(x)*h(x)]$ at $x=5$ = $g'(5) * h(5) + g(5) * h'(5)$ .
Substitute Values: Substitute the known values into the equation. $\newline$ $\frac{d}{dx}[g(x)*h(x)]$ at $x=5$ = $(-2)$ * $5$ + $7$ * $1$ .
Perform Multiplication: Perform the multiplication. $(d)/(dx)[g(x)*h(x)]$ at $x=5$ = $-10 + 7$ .
Add Results: Add the results to get the final answer. $\newline$ $\frac{d}{dx}[g(x)\cdot h(x)]$ at $x=5$ = $-3$ .