How do you differentiate # f(x) = sin^2 x#?

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Answer 1 · 2017-03-01T16:03:48

#2sinx*cosx#

It is helpful to write this function as
#f(x)=(sinx)^2#. Notice that both are equivalent.

Next differentiate using the chain rule.

Recall that the chain rule gives us a method to differentiate compositions. It is similar to the power but with an extra step

#d/(dx)f(g(x))=f'(g(x))*g'(x)#

For this function:
#f(x)=g(x)^2# and #g(x)=sinx#

If:

#d/(dx)f(x)=2g(x)^1# by the power rule

#d/(dx)sinx=cosx# (memorize this)

Then:
#d/(dx)(sinx)^2##=2sinx*cosx#