(d)/(dx)(x^((5)/(3)))=

Apply Power Rule: To find the derivative of $x^{\frac{5}{3}}$ with respect to $x$, we will use the power rule for differentiation. The power rule states that if $f(x) = x^n$, then $f'(x) = nx^{n-1}$.Calculate Exponent: Applying the power rule to $x^{\frac{5}{3}}$, we get $f'(x) = \frac{5}{3}x^{\frac{5}{3}-1}$.Simplify Exponent: Simplify the exponent by subtracting 1 from $\frac{5}{3}$. This gives us $f'(x) = \frac{5}{3}x^{\frac{5}{3}-\frac{3}{3}}$.Final Derivative: Simplify the exponent further to get $f'(x) = \frac{5}{3}x^{\frac{2}{3}}$.

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$\frac{d}{d x}\left(x^{\frac{5}{3}}\right)=$

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Algebra 2

Simplify variable expressions using properties

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\frac{d}{d x}\left(x^{\frac{5}{3}}\right)=

Apply Power Rule: To find the derivative of $x^{\frac{5}{3}}$ with respect to $x$ , we will use the power rule for differentiation. The power rule states that if $f(x) = x^n$ , then $f'(x) = nx^{n-1}$ .
Calculate Exponent: Applying the power rule to $x^{\frac{5}{3}}$ , we get $f'(x) = \frac{5}{3}x^{\frac{5}{3}-1}$ .
Simplify Exponent: Simplify the exponent by subtracting $1$ from $\frac{5}{3}$ . This gives us $f'(x) = \frac{5}{3}x^{\frac{5}{3}-\frac{3}{3}}$ .
Final Derivative: Simplify the exponent further to get $f'(x) = \frac{5}{3}x^{\frac{2}{3}}$ .