For the following equation, find f^(')(x). f(x)=4x^(2)-3x-9 Answer: f^(')(x)=

Apply Power Rule: To find the derivative of the function f(x) = 4x^2 - 3x - 9, we will use the power rule for differentiation. The power rule states that the derivative of x^n with respect to x is n*x^(n-1).Differentiate 4x^2: Applying the power rule to the first term 4x^2, we differentiate it as follows: The derivative of 4x^2 with respect to x is 2*4*x^(2-1) = 8x.Differentiate -3x: Next, we apply the power rule to the second term -3x, which is a linear term. The derivative of -3x with respect to x is simply the coefficient of x, which is -3.Differentiate -9: The third term -9 is a constant, and the derivative of a constant is 0.Combine Derivatives: Combining the derivatives of all three terms, we get the derivative of the function f(x): f'(x) = 8x - 3 + 0Simplify Final Result: Simplifying the expression, we see that the ＂+ 0＂ is unnecessary and can be omitted. The final derivative of the function f(x) is: f'(x) = 8x - 3

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For the following equation, find
f^(')(x).

f(x)=4x^(2)-3x-9
Answer:
f^(')(x)=

For the following equation, find $f^{\prime}(x)$ . $\newline$ $f(x)=4 x^{2}-3 x-9$ $\newline$ Answer: $f^{\prime}(x)=$

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Algebra 2

Composition of linear and quadratic functions: find an equation

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Q. For the following equation, find

f^{\prime}(x)

\newline

f(x)=4 x^{2}-3 x-9

\newline

Answer:

f^{\prime}(x)=

Apply Power Rule: To find the derivative of the function $f(x) = 4x^2 - 3x - 9$ , we will use the power rule for differentiation. The power rule states that the derivative of $x^n$ with respect to $x$ is $n\cdot x^{(n-1)}$ .
Differentiate $4x^2$ : Applying the power rule to the first term $4x^2$ , we differentiate it as follows: $\newline$ The derivative of $4x^2$ with respect to $x$ is $2\cdot4\cdot x^{(2-1)} = 8x$ .
Differentiate $-3x$ : Next, we apply the power rule to the second term $-3x$ , which is a linear term. The derivative of $-3x$ with respect to $x$ is simply the coefficient of $x$ , which is $-3$ .
Differentiate $-9$ : The third term $-9$ is a constant, and the derivative of a constant is $0$ .
Combine Derivatives: Combining the derivatives of all three terms, we get the derivative of the function $f(x)$ : $f'(x) = 8x - 3 + 0$
Simplify Final Result: Simplifying the expression, we see that the ＂+ $0$ ＂ is unnecessary and can be omitted. The final derivative of the function $f(x)$ is: $f'(x) = 8x - 3$