Question #e058f

1 Answer
jim p.
Nov 9, 2017

Use that dang ol' chain rule...

Explanation:

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

d/dx(cos^2(pi * x))ddx(cos2(π⋅x))

= 2cos(pi*x) * d/dx(cos(pi*x))=2cos(π⋅x)⋅ddx(cos(π⋅x))

= 2cos(pi*x) * (-sin(pi*x) * d/dx(pi*x))=2cos(π⋅x)⋅(−sin(π⋅x)⋅ddx(π⋅x))

= 2cos(pi*x) * pi(-sin(pi*x))=2cos(π⋅x)⋅π(−sin(π⋅x))

=-2pi(cos(pi*x) * sin(pi*x))=−2π(cos(π⋅x)⋅sin(π⋅x))

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

-pi(sin(2pi*x))−π(sin(2π⋅x))

GOOD LUCK

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