For the following equation, evaluate f^(')(1). f(x)=5x^(5)+2x^(3)+x Answer:

Identify Function: We need to find the derivative of the function f(x) = 5x^5 + 2x^3 + x with respect to x. This will give us f'(x), which we can then evaluate at x = 1.Apply Power Rule: Differentiate the function term by term using the power rule, which states that the derivative of x^n with respect to x is n*x^(n-1). f'(x) = d/dx [5x^5] + d/dx [2x^3] + d/dx [x] f'(x) = 5 * 5x^(5-1) + 2 * 3x^(3-1) + 1 * x^(1-1) f'(x) = 25x^4 + 6x^2 + 1Evaluate at x = 1: Evaluate the derivative at x = 1. f'(1) = 25(1)^4 + 6(1)^2 + 1 f'(1) = 25 + 6 + 1 f'(1) = 32

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For the following equation, evaluate
f^(')(1).

f(x)=5x^(5)+2x^(3)+x
Answer:

For the following equation, evaluate $f^{\prime}(1)$ . $\newline$ $f(x)=5 x^{5}+2 x^{3}+x$ $\newline$ Answer:

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Algebra 2

Find the vertex of the transformed function

Full solution

Q. For the following equation, evaluate

f^{\prime}(1)

\newline

f(x)=5 x^{5}+2 x^{3}+x

\newline

Answer:

Identify Function: We need to find the derivative of the function $f(x) = 5x^5 + 2x^3 + x$ with respect to $x$ . This will give us $f'(x)$ , which we can then evaluate at $x = 1$ .
Apply Power Rule: Differentiate the function term by term using the power rule, which states that the derivative of $x^n$ with respect to $x$ is $n*x^{(n-1)}$ . $\newline$ $f'(x) = \frac{d}{dx} [5x^5] + \frac{d}{dx} [2x^3] + \frac{d}{dx} [x]$ $\newline$ $f'(x) = 5 \cdot 5x^{(5-1)} + 2 \cdot 3x^{(3-1)} + 1 \cdot x^{(1-1)}$ $\newline$ $f'(x) = 25x^4 + 6x^2 + 1$
Evaluate at $x = 1$ : Evaluate the derivative at $x = 1$ .
$f'(1) = 25(1)^4 + 6(1)^2 + 1$
$f'(1) = 25 + 6 + 1$
$f'(1) = 32$