Chapter 4.2, Problem 34E

To determine

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

Answer to Problem 34E

  $\frac{dy}{dx}=\frac{1}{4}\times x^{\left(-\frac{3}{4}\right)}$

Explanation of Solution

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

  $y=\sqrt[4]{x}$

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

Calculation: Using the derivation,

  $\begin{array}{l}\frac{dy}{dx}=\frac{d\left(x^{\frac{1}{4}}\right)}{dx}\\ \frac{dy}{dx}=\frac{1}{4}\times x^{\left(\frac{1}{4}-1\right)}\\ \frac{dy}{dx}=\frac{1}{4}\times x^{\left(-\frac{3}{4}\right)}\end{array}$

So the derivative of y with respect to x is $\frac{dy}{dx}=\frac{1}{4}\times x^{\left(-\frac{3}{4}\right)}$ .