# How do you differentiate #f(x) = (sinx)/(x-e^x)# using the quotient rule?

As per the quotient rule,

Here,

Consequently, if we apply the quotient rule to differentiate, we obtain:

Although this can be simplified in other ways, each version is equally accurate.

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To differentiate f(x) = (sinx)/(x - e^x) using the quotient rule, first identify f'(x) = [g(x)*f'(x) - f(x)*g'(x)] / [g(x)]^2, where f(x) = sinx, g(x) = x - e^x, f'(x) = cosx, and g'(x) = 1 - e^x. Then substitute these values into the quotient rule formula and simplify to find the derivative of f(x).

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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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