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

Identify function & derivative: Identify the function and the derivative to be evaluated. We are given the function f(x) = -3x^5 + 3 and we need to find its derivative f'(x) at x = 1.Calculate derivative of function: Calculate the derivative of the function f(x). The derivative of f(x) = -3x^5 + 3 with respect to x is f'(x) = d/dx (-3x^5) + d/dx (3). Using the power rule for differentiation, the derivative of -3x^5 is -15x^4. The derivative of a constant, 3, is 0. So, f'(x) = -15x^4 + 0, which simplifies to f'(x) = -15x^4.Evaluate derivative at x=1: Evaluate the derivative at x = 1. Substitute x = 1 into the derivative f'(x) = -15x^4 to find f'(1). f'(1) = -15(1)^4 f'(1) = -15(1) f'(1) = -15

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

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

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

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Algebra 2

Composition of linear and quadratic functions: find a value

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Q. For the following equation, evaluate

f^{\prime}(1)

\newline

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

\newline

Answer:

Identify function & derivative: Identify the function and the derivative to be evaluated. $\newline$ We are given the function $f(x) = -3x^5 + 3$ and we need to find its derivative $f'(x)$ at $x = 1$ .
Calculate derivative of function: Calculate the derivative of the function $f(x)$ . The derivative of $f(x) = -3x^5 + 3$ with respect to $x$ is $f'(x) = \frac{d}{dx} (-3x^5) + \frac{d}{dx} (3)$ . Using the power rule for differentiation, the derivative of $-3x^5$ is $-15x^4$ . The derivative of a constant, $3$ , is $0$ . So, $f'(x) = -15x^4 + 0$ , which simplifies to $f'(x) = -15x^4$ .
Evaluate derivative at $x=1$ : Evaluate the derivative at $x = 1$ . Substitute $x = 1$ into the derivative $f'(x) = -15x^4$ to find $f'(1)$ . $f'(1) = -15(1)^4$ $f'(1) = -15(1)$ $f'(1) = -15$