How do you differentiate cos x all squared?

Answer 1

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The deriviative d/dx cos2(x) can be evaluated using the product rule.

Recall that d/dx f(x)g(x) = g(x) d/dx f(x) + f(x) d/dx g(x)

In this case, both f(x) and g(x) are cos(x), and cos2x = cos(x)cos(x), so...

d/dx cos(x)cos(x) = -cos(x)sin(x) - cos(x)sin(x) = -2sin(x)cos(x)