Problem 18 - College Algebra and Calculus: An Applied Approach

Question

Find the derivative of the function. $$ h(x)=x^{5 / 2} $$

Step-by-Step Solution

Answer

The derivative of the function \(h(x)=x^{5 / 2}\) is \(\frac{5}{2}x^{3/2}\).

Step 1: Identify the power rule

The power rule states that the derivative of \(x^n\) is \(n*x^{n-1}\). For the given function \(h(x)=x^{5 / 2}\), \(n=\frac{5}{2}\).

Step 2: Apply the power rule

By applying the power rule, the derivative of the function \(h(x)\) becomes \(\frac{5}{2}*x^{\frac{5}{2}-1}\).

Step 3: Simplify the result

Simplify the exponent by subtracting 1 from \(\frac{5}{2}\), this gives: \(\frac{5}{2}*x^{\frac{3}{2}}\) .