Let g(x)=x^((1)/(4)). g^(')(x)=

Identify Function: Identify the function to differentiate. We are given the function g(x) = x^(1/4) and we need to find its derivative, which is denoted by g'(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). Here, n = 1/4. So, g'(x) = (1/4)*x^(1/4 - 1).Simplify Exponent: Simplify the exponent. Subtract 1 from 1/4 to get the new exponent for x. 1/4 - 1 = 1/4 - 4/4 = -3/4. So, g'(x) = (1/4)*x^(-3/4).Write Final Answer: Write the final answer. The derivative of g(x) = x^(1/4) is g'(x) = (1/4)*x^(-3/4).

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Let $g(x)=x^{\frac{1}{4}}$ . $\newline$ $g^{\prime}(x)=$

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Algebra 1

Multiplication with rational exponents

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Q. Let

g(x)=x^{\frac{1}{4}}

\newline

g^{\prime}(x)=

Identify Function: Identify the function to differentiate. $\newline$ We are given the function $g(x) = x^{\frac{1}{4}}$ and we need to find its derivative, which is denoted by $g'(x)$ .
Apply Power Rule: Apply the power rule for differentiation. $\newline$ The power rule states that the derivative of $x^n$ with respect to $x$ is $n\cdot x^{n-1}$ . Here, $n = \frac{1}{4}$ . $\newline$ So, $g'(x) = \left(\frac{1}{4}\right)\cdot x^{\frac{1}{4} - 1}$ .
Simplify Exponent: Simplify the exponent. $\newline$ Subtract $1$ from $\frac{1}{4}$ to get the new exponent for $x$ . $\newline$ $\frac{1}{4} - 1 = \frac{1}{4} - \frac{4}{4} = -\frac{3}{4}$ . $\newline$ So, $g'(x) = (\frac{1}{4})*x^{-\frac{3}{4}}$ .
Write Final Answer: Write the final answer. $\newline$ The derivative of $g(x) = x^{\frac{1}{4}}$ is $g'(x) = \frac{1}{4} \cdot x^{-\frac{3}{4}}$ .