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

Apply Power Rule: To find the derivative of the function f(x) = -4x^4 + 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 -4x^4: Differentiate the term -4x^4. Using the power rule, the derivative of -4x^4 with respect to x is -4 * 4x^(4-1) which simplifies to -16x^3.Differentiate x: Differentiate the term x. The derivative of x with respect to x is 1, since the power rule states that the derivative of x^1 is 1 * x^(1-1) which simplifies to 1.Combine Derivatives: Combine the derivatives of the individual terms to find the derivative of the entire function. The derivative of f(x) = -4x^4 + x is f^(')(x) = -16x^3 + 1.

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

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

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

\newline

Answer:

f^{\prime}(x)=

Apply Power Rule: To find the derivative of the function $f(x) = -4x^4 + x$ , 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 $-4x^4$ : Differentiate the term $-4x^4$ . Using the power rule, the derivative of $-4x^4$ with respect to $x$ is $-4 \times 4x^{(4-1)}$ which simplifies to $-16x^3$ .
Differentiate $x$ : Differentiate the term $x$ . The derivative of $x$ with respect to $x$ is $1$ , since the power rule states that the derivative of $x^1$ is $1 \times x^{(1-1)}$ which simplifies to $1$ .
Combine Derivatives: Combine the derivatives of the individual terms to find the derivative of the entire function. The derivative of $f(x) = -4x^4 + x$ is $f^{\prime}(x) = -16x^3 + 1$ .