Chapter 6.3, Problem 7QR

To determine

To find: $\frac{dy}{dx}$

Answer to Problem 7QR

  $\frac{dy}{dx}=x^n$

Explanation of Solution

Given information: $y=\frac{x^{n+1}}{n+1},(n\ne -1)$

Calculation:

  $y=\frac{x^{n+1}}{n+1}$

Differentiating both sides of the equation with respect to x ,

  $\begin{array}{l}\frac{d}{dx}(y)=\frac{d}{dx}(\frac{x^{n+1}}{n+1})\\ =\frac{1}{n+1}\frac{d}{dx}(x^{n+1})[\because \frac{d}{dx}(cy)=c\frac{dy}{dx}]\\ =\frac{1}{n+1}\cdot (n+1)x^{(n+1)-1}[\because \frac{d}{dx}(x^n)=n{x}^{n-1}]\\ =x^n\end{array}$

Thus, $\frac{dy}{dx}=x^n$