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How do you differentiate #(2t +1)/(t + 3)#?

Answer 1

Paisley Johnson

I would use the Quotient Rule:

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Answer 2

Paisley Johnson

To differentiate (2t + 1)/(t + 3), you can use the quotient rule. The quotient rule states that if you have a function u(t) = f(t)/g(t), then the derivative du/dt is given by (g(t)*f'(t) - f(t)*g'(t)) / (g(t))^2. Applying this rule:

Let f(t) = 2t + 1 and g(t) = t + 3.

f'(t) = 2 (derivative of 2t is 2, derivative of 1 is 0) g'(t) = 1 (derivative of t is 1, derivative of 3 is 0)

Now, apply the quotient rule:

(2t + 1)' = ((t + 3)(2) - (2t + 1)(1)) / (t + 3)^2

= (2t + 6 - 2t - 1) / (t + 3)^2

= (5) / (t + 3)^2

So, the derivative of (2t + 1)/(t + 3) is 5/(t + 3)^2.

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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.