Can you help me find the derivative of y= cos(x)/1+sin(x).. the / is a fraction bar.

Question

I have a hard time finding trig derivatives because I don't really know what the derivative of cos,sin ,or tan would be honestly.

Answer 1

But, to even attempt this question, you MUST know the derivatives of the basic trig functions.

in this case, use the quotient rule

dy/dx = ( (1+sinx)(-sinx) - cosx(cosx) )/(1+sinx)^2
= (-sinx - sin^2 x - cos^2 x)/(1+sinx)^2
= (-sinx -1)(1+sinx)^2
= -(1+sinx)/(1+sinx)^2
= -1/(1+sinx)

Answer 2

Okay, I will get to familiarizing myself with the derivative of the trig functionss.

Thanks you so much, I really appreciate all the work and patience you tutors have :)