For the following equation, evaluate (dy)/(dx) when x=3. y=-x^(2)-3 Answer:

Identify function: Identify the function to differentiate. We are given the function y = -x^2 - 3 and we need to find its derivative with respect to x.Differentiate with respect to x: Differentiate the function with respect to x. The derivative of y with respect to x, denoted as (dy)/(dx), is found by differentiating each term of the function separately. (dy)/(dx) = d(-x^2)/dx - d(3)/dx The derivative of -x^2 with respect to x is -2x, and the derivative of a constant like -3 is 0. (dy)/(dx) = -2x - 0 (dy)/(dx) = -2xEvaluate at x=3: Evaluate the derivative at x=3. Substitute x=3 into the derivative to find the slope of the tangent line to the curve at that point. (dy)/(dx) at x=3 is -2(3). (dy)/(dx) at x=3 = -6

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For the following equation, evaluate
(dy)/(dx) when
x=3.

y=-x^(2)-3
Answer:

For the following equation, evaluate $\frac{d y}{d x}$ when $x=3$ . $\newline$ $y=-x^{2}-3$ $\newline$ Answer:

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Algebra 2

Composition of linear and quadratic functions: find a value

Full solution

Q. For the following equation, evaluate

\frac{d y}{d x}

when

x=3

\newline

y=-x^{2}-3

\newline

Answer:

Identify function: Identify the function to differentiate. $\newline$ We are given the function $y = -x^2 - 3$ and we need to find its derivative with respect to $x$ .
Differentiate with respect to x: Differentiate the function with respect to x. $\newline$ The derivative of $y$ with respect to $x$ , denoted as $\frac{dy}{dx}$ , is found by differentiating each term of the function separately. $\newline$ $\frac{dy}{dx} = \frac{d(-x^2)}{dx} - \frac{d(3)}{dx}$ $\newline$ The derivative of $-x^2$ with respect to $x$ is $-2x$ , and the derivative of a constant like $-3$ is $0$ . $\newline$ $\frac{dy}{dx} = -2x - 0$ $\newline$ $x$ $0$
Evaluate at $x=3$ : Evaluate the derivative at $x=3$ . Substitute $x=3$ into the derivative to find the slope of the tangent line to the curve at that point. $\frac{dy}{dx}$ at $x=3$ is $-2(3)$ . $\frac{dy}{dx}$ at $x=3$ = $-6$