How do you differentiate #y=2 csc x + 5 cos x#?
The derivative is
(I'm going to rearrange a few terms to make it easier to read.)
Rule of the quotient:
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To differentiate ( y = 2 \csc(x) + 5 \cos(x) ), you would use the rules of differentiation.
The derivative of ( \csc(x) ) is ( -\csc(x) \cot(x) ), and the derivative of ( \cos(x) ) is ( -\sin(x) ).
So, the derivative of ( 2\csc(x) ) is ( -2\csc(x)\cot(x) ), and the derivative of ( 5\cos(x) ) is ( -5\sin(x) ).
Therefore, the derivative of ( y = 2\csc(x) + 5\cos(x) ) is ( y' = -2\csc(x)\cot(x) - 5\sin(x) ).
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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.
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.
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.
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.

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