# What are the first two derivatives of #y = 2sin(3x) - 5sin(6x)#?

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The first derivative of ( y = 2\sin(3x) - 5\sin(6x) ) with respect to ( x ) is:

[ \frac{dy}{dx} = 6\cos(3x) - 30\cos(6x) ]

The second derivative is:

[ \frac{d^2y}{dx^2} = -18\sin(3x) + 180\sin(6x) ]

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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.

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