Question

How do you find the differential `dy` of the function `y=sec^2x/(x^2+1)`?

Answer 1

Compute the first derivative `dy/dx`, using the Quotient Rule .

Then multiply both sides by `dx`

Explanation:

Given `y=sec^2(x)/(x^2+1)`

Applying the Quotient Rule :

`dy/dx = (((d(sec^2(x)))/dx)(x^2+1)-sec^2(x)((d(x^2+1))/dx))/(x^2+1)^2`

`dy/dx = (2tan(x)sec^2(x)(x^2+1)-2xsec^2(x))/(x^2+1)^2`

Multiply both sides by `dx`:

`dy = (2tan(x)sec^2(x)(x^2+1)-2xsec^2(x))/(x^2+1)^2dx`