Chapter 4.2, Problem 31E

To determine

To calculate: The derivative of y with respect to x .

Answer to Problem 31E

  $\frac{dy}{dx}=\frac{9}{4}\times x^{\frac{5}{4}}$

Explanation of Solution

Given information: The equation of y in terms of x is given as,

  $y=x^{\frac{9}{4}}$

Formula Used: $\frac{d\left(x^n\right)}{dx}=n\times x^{\left(n-1\right)}$

Calculation:Using the derivation,

  $\begin{array}{l}\frac{dy}{dx}=\frac{d\left(x^{\frac{9}{4}}\right)}{dx}\\ \frac{dy}{dx}=\frac{9}{4}\times x^{\left(\frac{9}{4}-1\right)}\\ \frac{dy}{dx}=\frac{9}{4}\times x^{\frac{5}{4}}\end{array}$

So the derivative of y with respect to x is $\frac{dy}{dx}=\frac{9}{4}\times x^{\frac{5}{4}}$ .