# How do you differentiate #g(x) =e^x*1/x^2# using the product rule?

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To differentiate the function g(x) = e^x * 1/x^2 using the product rule, you apply the formula:

(d/dx) [f(x) * g(x)] = f'(x) * g(x) + f(x) * g'(x)

Where f(x) = e^x and g(x) = 1/x^2.

f'(x) = d/dx(e^x) = e^x g'(x) = d/dx(1/x^2) = -2/x^3

Now, applying the product rule:

g'(x) = e^x * 1/x^2 + e^x * (-2/x^3) = e^x / x^2 - 2e^x / 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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