Derivative of the sine and cosine functions. First Derivative. How can I simplify this expression ?
y=#sin^2# ( #pi# -x)
y=
1 Answer
Feb 28, 2017
The first derivative equals
Explanation:
This is equivalent to saying
#y = (sin(pi - x))(sin(pi - x))#
We can expand
#y = (sinpicosx - sinxcospi)(sinpicosx - sinxcospi)#
#y = (0(cosx) - sinx(-1))((0)cosx - (-1)sinx)#
#y= (sinx)(sinx)#
#y = (sinx)^2#
Now use the chain rule to differentiate. We let
#y' = 2u * cosx#
#y' = 2sinxcosx#
#y' = sin2x#
Hopefully this helps!