Biology homework help. ##d/dx (-csc(x)) = -d/dx(csc(x))##
Cosecant is the reciprocal of the sine function, so:
##-d/dx(1/sin(x))##
You should know that the derivative of ##1/x = -1/x^2##.
So by the : ##1/f(x) = -1/f(x)^2*d/dxf(x)##
Applying this here:
##-(-1/(sin^2(x))*d/dxsin(x))##
##= -(-1/(sin^2(x))*cos(x))##
## = cos(x)/(sin^2(x))d##
This is already an answer but in most textbooks, you see it in a different form:
## 1/sin(x) * cos(x)/sin(x)##
##= csc(x)*cot(x)##
I hope this helped you in any way.