# How do you find the derivative of #sinx/x#?

You can use the quotient rule or the product rule.

As you can see, you still get the same result in the end.

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To find the derivative of ( \frac{{\sin(x)}}{x} ), you can use the quotient rule. The quotient rule states that for functions ( u(x) ) and ( v(x) ), the derivative of ( \frac{{u(x)}}{v(x)} ) is given by:

[ \left( \frac{{u(x)}}{v(x)} \right)' = \frac{{u'(x)v(x) - u(x)v'(x)}}{(v(x))^2} ]

Applying this rule to ( \frac{{\sin(x)}}{x} ), where ( u(x) = \sin(x) ) and ( v(x) = x ), and noting that the derivative of ( \sin(x) ) is ( \cos(x) ), and the derivative of ( x ) is ( 1 ), the derivative of ( \frac{{\sin(x)}}{x} ) is:

[ \frac{{d}}{{dx}}\left(\frac{{\sin(x)}}{x}\right) = \frac{{(x \cdot \cos(x) - \sin(x) \cdot 1)}}{x^2} ]

Simplifying this expression gives:

[ \frac{{\cos(x) \cdot x - \sin(x)}}{x^2} ]

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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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