How do you differentiate #sin^2(3x)#?
We use the chain rule here
So
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To differentiate ( \sin^2(3  x) ):

Recognize that ( \sin^2(3  x) ) represents the square of the sine function of the expression ( (3  x) ).

Apply the chain rule, treating ( 3  x ) as the inner function.

Differentiate the outer function ( \sin^2(u) ) with respect to its inner function ( u ), and then multiply by the derivative of the inner function.

The derivative of ( \sin^2(u) ) with respect to ( u ) is ( 2\sin(u)\cos(u) ).

The derivative of ( 3  x ) with respect to ( x ) is ( 1 ).

Substitute ( u = 3  x ) into the derivative formula.

Differentiate the inner function ( u = 3  x ) to get ( du/dx = 1 ).

Combine the results from steps 4 and 7 to get the final derivative.
Therefore, the derivative of ( \sin^2(3  x) ) with respect to ( x ) is ( 2\sin(3  x)\cos(3  x) ).
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To differentiate sin^2(3x), you apply the chain rule and the power rule. The derivative is 2sin(3x)cos(3x).
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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