What is the value of (d)/(dx)((1)/(x^(4))) at x=2 ?

Identify Function: Identify the function to differentiate. We are given the function f(x) = 1/x^4 and we need to find its derivative with respect to 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). In this case, we can rewrite the function as f(x) = x^(-4) and then apply the power rule.Differentiate Function: Differentiate the function. Using the power rule, the derivative of f(x) = x^(-4) is f'(x) = -4*x^(-4-1) = -4*x^(-5).Simplify Derivative: Simplify the expression for the derivative. The simplified form of the derivative is f'(x) = -4/x^5.Evaluate at x=2: Evaluate the derivative at x=2. Substitute x=2 into the derivative to find its value at that point. f'(2) = -4/(2^5) = -4/32 = -1/8.

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What is the value of
(d)/(dx)((1)/(x^(4))) at
x=2 ?

What is the value of $\frac{d}{d x}\left(\frac{1}{x^{4}}\right)$ at $x=2$ ?

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Algebra 1

Multiplication with rational exponents

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Q. What is the value of

\frac{d}{d x}\left(\frac{1}{x^{4}}\right)

x=2

Identify Function: Identify the function to differentiate. $\newline$ We are given the function $f(x) = \frac{1}{x^4}$ and we need to find its derivative with respect to $x$ .
Apply Power Rule: Apply the power rule for differentiation. The power rule states that the derivative of $x^n$ with respect to $x$ is $n*x^{(n-1)}$ . In this case, we can rewrite the function as $f(x) = x^{-4}$ and then apply the power rule.
Differentiate Function: Differentiate the function. $\newline$ Using the power rule, the derivative of $f(x) = x^{-4}$ is $f'(x) = -4\cdot x^{-4-1} = -4\cdot x^{-5}$ .
Simplify Derivative: Simplify the expression for the derivative. $\newline$ The simplified form of the derivative is $f'(x) = -\frac{4}{x^5}$ .
Evaluate at $x=2$ : Evaluate the derivative at $x=2$ . $\newline$ Substitute $x=2$ into the derivative to find its value at that point. $\newline$ $f'(2) = -\frac{4}{(2^5)} = -\frac{4}{32} = -\frac{1}{8}$ .