Question

What is the derivative of `y= (cos pi x)/(sin pi x + cos pi x)`?

Answer 1

y'(x)= `(-pi)/(sinpix+cospix)`

Explanation:

using quotient rule,
y'(x)=`((sinpix + cospix)(-pisinpix)-(cospix)(picospix-pisinpix))/(sinpix+cospix)`
simplify and use `sin^2theta+ cos^2 theta=1`
we get, y'(x)= `(-pi)/(sinpix+cospix)`