# How do you find the equation of the tangent line to the graph of #f(x) = 2x ln(x + 2) # at x = 3?

You first need to differentiate

Using the product rule:

Let

Gradient at

Plot:

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To find the equation of the tangent line to the graph of f(x) = 2x ln(x + 2) at x = 3, we can follow these steps:

- Find the derivative of f(x) using the product rule and the chain rule.
- Evaluate the derivative at x = 3 to find the slope of the tangent line.
- Use the point-slope form of a line to write the equation of the tangent line.

Step 1: Find the derivative of f(x) f'(x) = 2(ln(x + 2) + x/(x + 2))

Step 2: Evaluate the derivative at x = 3 f'(3) = 2(ln(3 + 2) + 3/(3 + 2))

Step 3: Use the point-slope form to write the equation of the tangent line The equation of the tangent line is y - f(3) = f'(3)(x - 3).

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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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