What is the value of (d)/(dx)(x^((5)/(4))) at x=16 ?

Apply Power Rule: To find the derivative of x^(5/4) with respect to x, we will use the power rule for differentiation, which states that if f(x) = x^n, then f'(x) = n*x^(n-1).Calculate Derivative: Applying the power rule to x^(5/4), we get f'(x) = (5/4)*x^((5/4)-1) = (5/4)*x^(1/4).Substitute x=16: Now we need to evaluate the derivative at x=16. So we substitute x with 16 in the derivative we found: f'(16) = (5/4)*16^(1/4).Find Fourth Root: To simplify 16^(1/4), we need to find the fourth root of 16. The fourth root of 16 is 2 because 2^4 = 16.Substitute in Derivative: Substitute 16^(1/4) with 2 in the derivative: f'(16) = (5/4)*2.Final Derivative Value: Now we multiply (5/4) by 2 to get the final value of the derivative at x=16: f'(16) = (5/4)*2 = 5/2.

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What is the value of
(d)/(dx)(x^((5)/(4))) at
x=16 ?

What is the value of $\frac{d}{d x}\left(x^{\frac{5}{4}}\right)$ at $x=16$ ?

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Q. What is the value of

\frac{d}{d x}\left(x^{\frac{5}{4}}\right)

x=16

Apply Power Rule: To find the derivative of $x^{\frac{5}{4}}$ with respect to $x$ , we will use the power rule for differentiation, which states that if $f(x) = x^n$ , then $f'(x) = n \cdot x^{n-1}$ .
Calculate Derivative: Applying the power rule to $x^{5/4}$ , we get $f'(x) = \frac{5}{4} \cdot x^{\left(\frac{5}{4}-1\right)} = \frac{5}{4} \cdot x^{1/4}$ .
Substitute $x=16$ : Now we need to evaluate the derivative at $x=16$ . So we substitute $x$ with $16$ in the derivative we found: $f'(16) = (\frac{5}{4})\cdot16^{\frac{1}{4}}$ .
Find Fourth Root: To simplify $16^{1/4}$ , we need to find the fourth root of $16$ . The fourth root of $16$ is $2$ because $2^4 = 16$ .
Substitute in Derivative: Substitute $16^{1/4}$ with $2$ in the derivative: $f'(16) = \frac{5}{4}\cdot2$ .
Final Derivative Value: Now we multiply $(\frac{5}{4})$ by $2$ to get the final value of the derivative at $x=16$ : $f'(16) = (\frac{5}{4})\cdot2 = \frac{5}{2}$ .