How to find the derivative of cos^2x? i seem to be confused.
i was told to use the chain rule, but i don't see how it can apply.
can't i just substitute (cos x(cos x in its place and then use the product rule? isn't cos^2 x = (cos x(cos x?
let me know if i am right. if not, then explain how to use the chain rule ; how are you getting: ?

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You can actually use either the product rule or the chain rule for this one. Observe:

•  Method I:

y = cos² x

y = cos x · cos x

Differentiate it by applying the product rule:



The derivative of  cos x  is  – sin x. So you have





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•  Method II:

You can also treat  y  as a composite function:



and then, differentiate  y  by applying the chain rule:



For that first derivative with respect to  u, just use the power rule, then you have



and then you get the same



I hope this helps. =)

Tags:  derivative chain rule product rule composite function trigonometric trig squared cosine cos differential integral calculus