Asked by Angel
Can you help me find the derivative of y= cos(x)/1+sin(x).. the / is a fraction bar.
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.
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.
Answers
Answered by
Reiny
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)
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)
Answered by
Angel
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 :)
Thanks you so much, I really appreciate all the work and patience you tutors have :)