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Find the derivatives of the given functions.$$y=2 \ln \left(3 x^{2}-1\right)$$

$\frac{d u}{d x}=\frac{12 x}{3 x^{2}-1}$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 5

Derivative of the Logarithmic Function

Derivatives

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uh huh We want to find the derivative dy dx for the function. Why is equal to two times natural algorithm of three X squared plus one to do so we're going to rely on differentiation shortcuts. We picked up a single variable count in particular those related to the algorithms and natural algorithms. So I have listed the relevant rules for driven taking here on the left. We have rules zero for taking the X log B of U and G D f L M A view on the right. We have the power rule, product rule and change respectively. And this problem we need to use rule zero for natural algorithm. Um you as well as implicitly the chain rule. So why equals to Ellen three experiments, one has already written in the most easily dispensable forum. You is three experiments. One we have a factor of two outside as such we need to get rid of. So do I. D X is two times one over. You won over three experiments. One times duty X six X. Simplifying and multiplying are constants. Gives final solution. Do Y? The X is equal to 12 X, divided by three x squared minus one.

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