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How do you find the derivative of #y = cos 2x#?

Answer 1

Ezekiel Alexander

# dy/dx = -2sin2x #

This is an example of a function 2x inside a cos function.

We call this function of a function.

Differentiating cosx yields - sinx.

We obtain - sin2x when we differentiate cos2x, but we still need to differentiate 2x.

You can express this as y = cos2x.

# rArr dy/dx = - sin2x . d/dx (2x )= - sin2x . 2 #

#rArr dy/dx = -2sin2x #

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Answer 2

Emilia Aguilar

To find the derivative of ( y = \cos(2x) ), you can apply the chain rule of differentiation, which states that the derivative of a composition of functions is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function. In this case, the outer function is cosine and the inner function is ( 2x ).

So, the derivative of ( \cos(2x) ) is ( -\sin(2x) ) multiplied by the derivative of ( 2x ), which is ( 2 ). Therefore, the derivative of ( y = \cos(2x) ) is ( \frac{dy}{dx} = -2\sin(2x) ).

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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.