Question

How do you integrate `g(x)=sinx/x^2` using the quotient rule?

Answer 1

See explanation.

Explanation:

From the topic you wrote in I assume you mean "how to differentiate the function?"

The Quotient Rule says that if `f(x)` and `g(x)` are continuous functions, then to calculate the derivative `[(f(x))/g(x)]'` you can use the following formula:

`[(f(x))/g(x)]'=(f'(x)g(x)-f(x)g'(x))/g^2(x)`

For the given function the derivative is:

`[sinx/x^2]'=((sinx)'*x^2-(x^2)'sinx)/x^4=(cosx*x^2-2xsinx)/x^4=(xcosx-x2sinx)/x^4=`

`= (cosx-2sinx)/x^3`