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

1 Answer
Daniel L.
Dec 11, 2016

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#

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