How do i do the anti-derivative?

#dx/dy# sin(x/2)

1 Answer
Sep 24, 2017

Assuming the question is #dy/dx=sin(x/2)#, the answer is #y=-2cos(x/2)#

Explanation:

First, work out what trig function it's coming from. Sin differentiates to negative #cos#, so therefore negative #sin# differentiates to positive #cos#.

Next divide by the differential of what's in the bracket.
In the bracket: #(x/2)# #:.# derivative of that is just #(1/2)#

#-cos(1/2x)# divided by a half #= -2cos(x/2)# which is your answer.