Question #e058f

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Question #e058f

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Answer 1 · 2017-11-09T17:59:56

Use that dang ol' chain rule...

Explanation:

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

$\frac{d}{d x} ({cos}^{2} (π \cdot x))$ $d/dx(cos^2(pi * x))$

$= 2 cos (π \cdot x) \cdot \frac{d}{d x} (cos (π \cdot x))$ $= 2cos(pi*x) * d/dx(cos(pi*x))$

$= 2 cos (π \cdot x) \cdot (- sin (π \cdot x) \cdot \frac{d}{d x} (π \cdot x))$ $= 2cos(pi*x) * (-sin(pi*x) * d/dx(pi*x))$

$= 2 cos (π \cdot x) \cdot π (- sin (π \cdot x))$ $= 2cos(pi*x) * pi(-sin(pi*x))$

$= - 2 π (cos (π \cdot x) \cdot sin (π \cdot x))$ $=-2pi(cos(pi*x) * sin(pi*x))$

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

$- π (sin (2 π \cdot x))$ $-pi(sin(2pi*x))$

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Question #e058f

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