# How do you differentiate #(t^2+2)/(6t-3)^7#?

We must use the quotient rule, which states that

Now, before starting, we can acknowledge all our four needed functions:

Thus,

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To differentiate (t^2 + 2) / (6t - 3)^7, you would apply the quotient rule of differentiation. The quotient rule states that if you have a function of the form f(x) / g(x), then its derivative is given by [g(x)f'(x) - f(x)g'(x)] / [g(x)]^2. Using this rule:

- Find the derivative of the numerator: f'(x) = 2t.
- Find the derivative of the denominator: g'(x) = 6.
- Substitute these derivatives into the quotient rule formula: [6t(6t - 3)^7 - (t^2 + 2)(6)] / (6t - 3)^14.

This simplifies to:

[12t(6t - 3)^7 - 6(t^2 + 2)] / (6t - 3)^14.

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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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