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Differentiate the function? f(x) = ln(x^6 + 4)

Answer 1

Christopher Agresta

The answer is #=(6x^5)/(x^6+4)#

Apply the following (chain rule) for the differentiation

#f(x)=ln(u(x))#

#f'(x)=1/(u(x))*u'(x)#

Here,

#f(x)=ln(x^6+4)#

#f'(x)=1/(x^6+4)*(x^6+4)'#

#=(6x^5)/(x^6+4)#

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Answer 2

Isabella Ackerman

To differentiate the function ( f(x) = \ln(x^6 + 4) ), we use the chain rule.

The derivative of ( \ln(u) ) with respect to ( x ) is ( \frac{1}{u} \cdot \frac{du}{dx} ), where ( u ) is a function of ( x ).

In this case, let ( u = x^6 + 4 ). So, ( \frac{du}{dx} = 6x^5 ).

Therefore, the derivative of ( f(x) ) is:

[ f'(x) = \frac{1}{x^6 + 4} \cdot 6x^5 ]

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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.