How do you find the derivative of #y = 3 / (cos2x^2)#?
Rewrite the problem as:
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To find the derivative of ( y = \frac{3}{\cos^2(2x^2)} ), you would use the chain rule. The derivative is ( \frac{-12x \sin(4x^2)}{\cos^3(2x^2)} ).
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To find the derivative of ( y = \frac{3}{\cos(2x^2)} ), you can use the chain rule along with the derivative of the cosine function. The chain rule states that if ( y = f(g(x)) ), then ( y' = f'(g(x)) \cdot g'(x) ).
Let ( u = 2x^2 ), then ( y = \frac{3}{\cos(u)} ).
Using the chain rule:
[ y' = -3 \cdot \frac{\sin(u)}{\cos^2(u)} \cdot \frac{d}{dx}(2x^2) ]
Now, find the derivative of ( u ) with respect to ( x ):
[ \frac{d}{dx}(2x^2) = 4x ]
Substitute ( u = 2x^2 ) back into the expression:
[ y' = -3 \cdot \frac{\sin(2x^2)}{\cos^2(2x^2)} \cdot 4x ]
Thus, the derivative of ( y = \frac{3}{\cos(2x^2)} ) is:
[ y' = -12x \cdot \frac{\sin(2x^2)}{\cos^2(2x^2)} ]
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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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