# How do you differentiate # y= log (6x-2)#?

Now differentiation will be relatively easy.

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To differentiate ( y = \log(6x - 2) ), you can use the chain rule of differentiation. The chain rule states that if you have a function ( f(g(x)) ), then the derivative is ( f'(g(x)) \cdot g'(x) ). Applying this to the given function:

- Identify the inner function: ( g(x) = 6x - 2 ).
- Find the derivative of the inner function: ( g'(x) = 6 ).
- Determine the derivative of the outer function, which is ( f(u) = \log(u) ): ( f'(u) = \frac{1}{u} ).
- Substitute back into the chain rule formula: ( y' = \frac{1}{6x - 2} \cdot 6 ).

Simplifying the expression, we get ( y' = \frac{6}{6x - 2} ), which can be further simplified to ( y' = \frac{6}{2(3x - 1)} ) or ( y' = \frac{3}{3x - 1} ).

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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.

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.

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.

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