Let f(x)=x^((3)/(2)). f^(')(x)=

Identify Function & Operation: Identify the function and the operation to be performed. We have the function f(x) = x^(3/2) 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 if f(x) = x^n, then f'(x) = n*x^(n-1). Here, n = 3/2.Differentiate Using Rule: Differentiate the function using the power rule. f'(x) = (3/2) * x^((3/2) - 1)Simplify Exponent: Simplify the exponent. f'(x) = (3/2) * x^(1/2)Write Final Derivative: Write the final expression for the derivative. f'(x) = (3/2) * sqrt(x)

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Let $f(x)=x^{\frac{3}{2}}$ . $\newline$ $f^{\prime}(x)=$

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Q. Let

f(x)=x^{\frac{3}{2}}

\newline

f^{\prime}(x)=

Identify Function & Operation: Identify the function and the operation to be performed. $\newline$ We have the function $f(x) = x^{(3/2)}$ and we need to find its derivative, which is denoted by $f'(x)$ .
Apply Power Rule: Apply the power rule for differentiation. $\newline$ The power rule states that if $f(x) = x^n$ , then $f'(x) = n\cdot x^{(n-1)}$ . Here, $n = \frac{3}{2}$ .
Differentiate Using Rule: Differentiate the function using the power rule. $\newline$ $f'(x) = \frac{3}{2} \cdot x^{\left(\frac{3}{2} - 1\right)}$
Simplify Exponent: Simplify the exponent. $f'(x) = \frac{3}{2} \cdot x^{\frac{1}{2}}$
Write Final Derivative: Write the final expression for the derivative. $f'(x) = \frac{3}{2} \cdot \sqrt{x}$