# How do you find the slope of the tangent line to the graph of the function #f(x)= x*e^x# at x=7?

So, we differentiate using the product rule, which states that,

And so, we got:

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To find the slope of the tangent line to the graph of the function f(x) = x*e^x at x = 7, we can use the derivative of the function. The derivative of f(x) with respect to x is given by f'(x) = (1 + x)*e^x.

To find the slope of the tangent line at x = 7, we substitute x = 7 into the derivative function f'(x).

f'(7) = (1 + 7)*e^7 = 8*e^7

Therefore, the slope of the tangent line to the graph of f(x) = x*e^x at x = 7 is 8*e^7.

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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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