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

1 Answer
Oct 2, 2017

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