Home > Calculus > Derivative Rules for y=cos(x) and y=tan(x)

How do you differentiate #y = cos^3(3x+1)#?

Answer 1

I would use the Chain Rule deriving the #()^3# first and then the #cos# and then the argument as: #y'=3cos^2(3x+1)*[-sin(3x+1)]*3=-9cos^2(3x+1)sin(3x+1)#

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Answer 2

Cameron Alexander

To differentiate ( y = \cos^3(3x+1) ), you can use the chain rule. The derivative is:

[ \frac{dy}{dx} = -3\sin(3x+1)\cos^2(3x+1) ]

This result comes from applying the chain rule, where the derivative of the outer function (( \cos^3 )) is ( -3\sin(3x+1) ) and the derivative of the inner function (( 3x+1 )) is ( 3 ).

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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.