#### To determine

**To find:** The value of *y*.

#### Answer

The value of *y* is 2.

#### Explanation

**Given:**

The rate of change of y5 with respect to *x* eighty times the rate of change of *y* with

respect to *x.* That is, ddx(y5)=80dydx (1)

**Calculation:**

The derivative ddx(y5) is computed as follows,

ddx(y5)=ddy(y5)⋅dydx=(5y5−1)dydx=5y4dydx

From equation (1), 5y4dydx=80dydx.

Here, dydx≠0 since the curve never has a horizontal tangent.

5y4=80y4=16y4=24y=2

Therefore, the value of *y* is 2.