For the following equation, find f^(')(x). f(x)=-8x^(3)+x Answer: f^(')(x)=

Apply Power Rule: To find the derivative of the function f(x) = -8x^3 + x, we will apply 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 -8x^3: Differentiate the term -8x^3. Using the power rule, the derivative of -8x^3 is -8 * 3 * x^(3-1) = -24x^2.Differentiate x: Differentiate the term x. The derivative of x with respect to x is 1, since the power rule gives us 1 * x^(1-1) = 1 * x^0 = 1.Combine Derivatives: Combine the derivatives of both terms to get the derivative of the entire function. Therefore, f'(x) = -24x^2 + 1.

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

f(x)=-8x^(3)+x
Answer:
f^(')(x)=

For the following equation, find $f^{\prime}(x)$ . $\newline$ $f(x)=-8 x^{3}+x$ $\newline$ Answer: $f^{\prime}(x)=$

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Algebra 2

Evaluate exponential functions

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Q. For the following equation, find

f^{\prime}(x)

\newline

f(x)=-8 x^{3}+x

\newline

Answer:

f^{\prime}(x)=

Apply Power Rule: To find the derivative of the function $f(x) = -8x^3 + x$ , we will apply 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 $-8x^3$ : Differentiate the term $-8x^3$ . Using the power rule, the derivative of $-8x^3$ is $-8 \times 3 \times x^{(3-1)} = -24x^2$ .
Differentiate $x$ : Differentiate the term $x$ . The derivative of $x$ with respect to $x$ is $1$ , since the power rule gives us $1 \times x^{1-1} = 1 \times x^0 = 1$ .
Combine Derivatives: Combine the derivatives of both terms to get the derivative of the entire function. Therefore, $f'(x) = -24x^2 + 1$ .