For the following equation, find f^(')(x). f(x)=7x^(5)+5 Answer: f^(')(x)=

Identify Function: Identify the function to differentiate. We are given the function f(x) = 7x^5 + 5, and we need to find its derivative, which is denoted by f^(')(x).Apply Power Rule: 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). We will apply this rule to the term 7x^5.Differentiate 7x^5: Differentiate the term 7x^5. Using the power rule, the derivative of 7x^5 is 5 * 7x^(5-1) = 35x^4.Differentiate Constant: Differentiate the constant term 5. The derivative of a constant is 0, so the derivative of 5 with respect to x is 0.Combine Derivatives: Combine the derivatives of all terms to find f^(')(x). f^(')(x) = 35x^4 + 0 Simplify the expression by removing the 0. f^(')(x) = 35x^4

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

f(x)=7x^(5)+5
Answer:
f^(')(x)=

For the following equation, find $f^{\prime}(x)$ . $\newline$ $f(x)=7 x^{5}+5$ $\newline$ Answer: $f^{\prime}(x)=$

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Algebra 2

Find the vertex of the transformed function

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Q. For the following equation, find

f^{\prime}(x)

\newline

f(x)=7 x^{5}+5

\newline

Answer:

f^{\prime}(x)=

Identify Function: Identify the function to differentiate. $\newline$ We are given the function $f(x) = 7x^5 + 5$ , and we need to find its derivative, which is denoted by $f^{\prime}(x)$ .
Apply Power Rule: Apply the power rule for differentiation. The power rule states that the derivative of $x^n$ with respect to $x$ is $n*x^{(n-1)}$ . We will apply this rule to the term $7x^5$ .
Differentiate $7x^5$ : Differentiate the term $7x^5$ . Using the power rule, the derivative of $7x^5$ is $5 \times 7x^{(5-1)} = 35x^4$ .
Differentiate Constant: Differentiate the constant term $5$ . The derivative of a constant is $0$ , so the derivative of $5$ with respect to $x$ is $0$ .
Combine Derivatives: Combine the derivatives of all terms to find $f'(x)$ . $f'(x) = 35x^4 + 0$ Simplify the expression by removing the $0$ . $\$f'(x) = 35x^4$ )