For the following equation, find f^(')(x). f(x)=-4x^(4)-8 Answer: f^(')(x)=

Apply Power Rule: To find the derivative of the function f(x) = -4x^4 - 8, we will use the power rule for differentiation. The power rule states that if f(x) = x^n, then f^(')(x) = n*x^(n-1).Differentiate -4x^4: Applying the power rule to the term -4x^4, we differentiate it as follows: f^(')(x) for -4x^4 = -4 * 4 * x^(4-1) = -16x^3.Derivative of Constant: The derivative of a constant is zero. Therefore, the derivative of -8 is 0.Combine Derivatives: Combining the derivatives of both terms, we get the derivative of the entire function: f^(')(x) = -16x^3 + 0.Simplify Final Result: Simplifying the expression, we get the final derivative of the function: f^(')(x) = -16x^3.

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

f(x)=-4x^(4)-8
Answer:
f^(')(x)=

For the following equation, find $f^{\prime}(x)$ . $\newline$ $f(x)=-4 x^{4}-8$ $\newline$ Answer: $f^{\prime}(x)=$

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Algebra 2

Evaluate expression when a complex numbers and a variable term is given

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Q. For the following equation, find

f^{\prime}(x)

\newline

f(x)=-4 x^{4}-8

\newline

Answer:

f^{\prime}(x)=

Apply Power Rule: To find the derivative of the function $f(x) = -4x^4 - 8$ , we will use the power rule for differentiation. The power rule states that if $f(x) = x^n$ , then $f^{\prime}(x) = n \cdot x^{n-1}$ .
Differentiate $-4x^4$ : Applying the power rule to the term $-4x^4$ , we differentiate it as follows: $\newline$ $f'(x)$ for $-4x^4 = -4 \times 4 \times x^{4-1} = -16x^3$ .
Derivative of Constant: The derivative of a constant is zero. Therefore, the derivative of $-8$ is $0$ .
Combine Derivatives: Combining the derivatives of both terms, we get the derivative of the entire function: $\newline$ $f^{\prime}(x) = -16x^3 + 0$ .
Simplify Final Result: Simplifying the expression, we get the final derivative of the function: $f'(x) = -16x^3$ .