How do you find the derivative of #2cos^2(x)#?

Answer 1

Emily Ammerman

#-2sin2x#

#"differentiate using the "color(blue)"chain rule"#

#"Given "y=f(g(x))" then"#

#dy/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"#

#y=2cos^2x=2(cosx)^2#

#rArrdy/dx=4cosx xxd/dx(cosx)#

#color(white)(rArrdy/dx)=-4sinxcosx=-2sin2x#

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Answer 2

Luke Alvarez

To find the derivative of (2\cos^2(x)), you can use the chain rule and the derivative of cosine function.

(2\cos^2(x)) can be rewritten as (2(\cos(x))^2).

The derivative of (\cos(x)) is (-\sin(x)).

Apply the chain rule: (\frac{d}{dx}(\cos(x))^2 = 2\cos(x)(-\sin(x))).

So, the derivative of (2\cos^2(x)) is (2\cos(x)(-\sin(x)) = -2\cos(x)\sin(x)).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.