derivative of cos^2(x)
2cosx sinx
To find the derivative of cos^2(x), we can use the chain rule and the power rule of differentiation.
First, let’s rewrite cos^2(x) as cos(x) * cos(x).
Then, using the chain rule, we find that the derivative of cos(x) * cos(x) with respect to x is:
(cos(x))’ * cos(x) + cos(x) * (cos(x))’
Now, we know that the derivative of cos(x) with respect to x is equal to -sin(x). So we can replace (cos(x))’ with -sin(x):
– sin(x) * cos(x) + cos(x) * -sin(x)
Using the distributive property, we can simplify this to:
-2 sin(x) cos(x)
Therefore, the derivative of cos^2(x) with respect to x is -2 sin(x) cos(x).
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