Question #e058f

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Answer 1 · 2017-11-09T17:59:56

Use that dang ol' chain rule...

...but you have to apply it more than once...

#d/dx(cos^2(pi * x))#

# = 2cos(pi*x) * d/dx(cos(pi*x))#

# = 2cos(pi*x) * (-sin(pi*x) * d/dx(pi*x))#

# = 2cos(pi*x) * pi(-sin(pi*x))#

#=-2pi(cos(pi*x) * sin(pi*x))#

(Wolfram reminds me that you can use the double angle identity - #2cos(a)sin(a) = sin(2a)#, so you can rewrite the above as:

#-pi(sin(2pi*x))#

GOOD LUCK