# How do you differentiate #y=sinx/x^2#?

We have

We can differentiate it by two methods:

Method 1:

We will use the quotient rule, there is a way I like to remember it:

Denominator same, differentiation of numerator. Minus numerator same, differentiation of denominator whole divided by denominator squared

Differentiating with respect to x:

Method 2:

Simplifying:

We can now apply the product rule, there is a way I like to remember it:

First function same, differentiation of second function. Plus second function same, differentiation of first function

Differentiating with respect to x:

Rearranging the terms, we get:

I hope it helps!

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To differentiate ( y = \frac{\sin(x)}{x^2} ), you can use the quotient rule:

[ \frac{d}{dx} \left( \frac{u}{v} \right) = \frac{vu' - uv'}{v^2} ]

Where ( u = \sin(x) ) and ( v = x^2 ).

[ u' = \cos(x) \quad \text{and} \quad v' = 2x ]

Now, plug these values into the quotient rule:

[ \frac{d}{dx} \left( \frac{\sin(x)}{x^2} \right) = \frac{x^2 \cos(x) - 2x \sin(x)}{x^4} ]

Simplify the expression:

[ \frac{d}{dx} \left( \frac{\sin(x)}{x^2} \right) = \frac{x \cos(x) - 2 \sin(x)}{x^3} ]

So, the derivative of ( y = \frac{\sin(x)}{x^2} ) is ( \frac{x \cos(x) - 2 \sin(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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