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How do you find the derivative of #cos2x^4#?

Answer 1

Luke Alvarez

Refer to explanation

It is

#y=cos2x^4=>dy/dx=-sin(2x^4)*(2x^4)'=-8x^3*sin(2x^4)#

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Answer 2

Emily Ammerman

To find the derivative of ( \cos(2x^4) ), you would use the chain rule. The derivative can be found by taking the derivative of the outer function (( \cos )) and then multiplying it by the derivative of the inner function (( 2x^4 )).

So, the derivative of ( \cos(2x^4) ) is:

[ -\sin(2x^4) \times \frac{d}{dx}(2x^4) ]

Applying the chain rule:

[ -\sin(2x^4) \times (2 \cdot 4x^3) ]

[ -8x^3\sin(2x^4) ]

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Answer from HIX Tutor

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.