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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 answer:
I hope this helps. =)
Tags: <em>derivative chain rule product rule composite function trigonometric trig squared cosine cos differential integral calculus</em>
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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
—————
• 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 answer:
I hope this helps. =)
Tags: <em>derivative chain rule product rule composite function trigonometric trig squared cosine cos differential integral calculus</em>