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Chapter 7: Problem 18

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

Short Answer

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

Step by step solution

01

Identify the power rule

The power rule states that the derivative of \(x^n\) is \(n*x^{n-1}\). For the given function \(h(x)=x^{5 / 2}\), \(n=\frac{5}{2}\).
02

Apply the power rule

By applying the power rule, the derivative of the function \(h(x)\) becomes \(\frac{5}{2}*x^{\frac{5}{2}-1}\).
03

Simplify the result

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

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Most popular questions from this chapter

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