# How do you differentiate #f(x)=sinx/x#?

The Quotient Rule for Diffn. states that,

Here,

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We can use the quotient rule:

where

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To differentiate ( f(x) = \frac{{\sin(x)}}{{x}} ), you can use the quotient rule.

Quotient rule states:

If ( f(x) = \frac{{g(x)}}{{h(x)}} ), then ( f'(x) = \frac{{g'(x)h(x) - g(x)h'(x)}}{{[h(x)]^2}} ).

For ( f(x) = \frac{{\sin(x)}}{{x}} ):

( g(x) = \sin(x) ) and ( h(x) = x ).

( g'(x) = \cos(x) ) (derivative of sine function) and ( h'(x) = 1 ) (derivative of ( x )).

Apply the quotient rule:

( f'(x) = \frac{{\cos(x) \cdot x - \sin(x) \cdot 1}}{{x^2}} )

( f'(x) = \frac{{x \cos(x) - \sin(x)}}{{x^2}} )

So, ( f'(x) = \frac{{x \cos(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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