Question

find dy/dx, if y=sinx/1+cosx​

Answer 1

Answer:

Use the division's derivative formula:

For a given function g: g=uv for u and v≠0 other functions, the derivative of g is found as;

g'=u'v−uv'v2

If we apply it to our case:

f'(x)=(sinx)'(1+cosx)−sinx(1+cosx)'(1+cosx)2=cosx(1+cosx)+sinxsinx(1+cosx)2=cosx+cos2x+sin2x(1+cosx)2

Using now the trigonometric rule: cos2x+sin2x=1 we finally get:

f'(x)=1+cosx(1+cosx)2=11+cosx