How do you differentiate #y=cosln4x^3#?

Answer 1

Christopher Agresta

#dy/dx=(-3sin(ln(4x^3)))/x#

#y=cosln4x^3#

Use chain rule #(f(g(x))' = f'(g(x)) * g'(x)#

#dy/dx=-sin(ln(4x^3))*1/(4x^3) *12x^2#

#dy/dx=-sin(ln(4x^3)) *3/x#

#dy/dx=(-3sin(ln(4x^3)))/x#

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Answer 2

Isabella Ackerman

To differentiate ( y = \cos(\ln(4x^3)) ), you would use the chain rule. The derivative is given by:

[ \frac{dy}{dx} = -\sin(\ln(4x^3)) \cdot \frac{1}{4x^3} \cdot 3 \cdot 4x^2 ]

Simplified:

[ \frac{dy}{dx} = -3\sin(\ln(4x^3)) \cdot x^{-1} ]

So, the derivative of ( y = \cos(\ln(4x^3)) ) with respect to ( x ) is ( -3\sin(\ln(4x^3)) \cdot x^{-1} ).

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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.