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How do you find the derivative of #f(x)=ln(3x^(2)+6x+5)#?

Answer 1

Aurora Alvarado

#(6(x+1))/(3x^(2)+6x+5)#

#f(x)=ln(3x^(2)+6x+5)#

as a general matter if #y = ln ( f(x) )# then #y' = 1/(f(x)) f'(x)# [chain rule]

here #f'(x)=1/(3x^(2)+6x+5)(3x^(2)+6x+5)'# #=(6x+6)/(3x^(2)+6x+5)#

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Answer 2

Evelyn Agard

To find the derivative of ( f(x) = \ln(3x^2 + 6x + 5) ), you can use the chain rule. The derivative is ( f'(x) = \frac{1}{3x^2 + 6x + 5} \cdot \frac{d}{dx}(3x^2 + 6x + 5) ). Differentiating ( 3x^2 + 6x + 5 ) with respect to ( x ) yields ( 6x + 6 ). So, ( f'(x) = \frac{6x + 6}{3x^2 + 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.