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

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Answer 1 · 2017-10-02T19:16:45

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

Then multiply both sides by #dx#

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#