Question #7f6d8

1 Answer
Oct 13, 2017

I personally like to rewrite functions to make it easier to use the product rule instead of the quotient rule where applicable.

Let #f(x) = cos^2(x)/sqrt(cos2x)#

#= cos^2(x)*(cos2x)^(-1/2)#

Here we can see we will use the chain rule and product rule to differentiate.

#d/dxf(x)= -2cos(x)sin(x)*(cos(2x))^(-1/2) + cos^2(x)(-1/2)cos(2x)^(-3/2)(-sin(2x))(2)#


#=(cos^2(x)sin(2x))/(cos(2x)^(3/2)) - (2cos(x)sin(x))/(sqrtcos(2x))#

(I moved the negative fraction to the back to avoid having a negative up front)

You could simplify this further if you wanted just one fraction, you can just use your arithmetic skills for that.