What is the derivative of #sin^2(x)#?
You would use the chain rule to solve this. To do that, you'll have to determine what the "outer" function is and what the "inner" function composed in the outer function is.
In this case,
So, mathematically, the chain rule is:
The derivative of a composite function F(x) is:
Or, in words:
the derivative of the outer function (with the inside function left alone!) times the derivative of the inner function.
1) The derivative of the outer function(with the inside function left alone) is:
#d/dx u^2= 2u#
(I'm leaving the
#u#in for now but you can sub in #u=sin(x)#if you want to while you're doing the steps. Remember that these are just steps, the actual derivative of the question is shown at the bottom)
2) The derivative of the inner function:
#d/dx sin (x) = cos (x)#
Combining the two steps through multiplication to get the derivative:
#d/dx sin^2(x)=2ucos (x)=2sin(x)cos(x)#