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

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 $f \left(x\right)$ and $g \left(x\right)$ are continuous functions, then to calculate the derivative $\left[\frac{f \left(x\right)}{g} \left(x\right)\right] '$ you can use the following formula:

$\left[\frac{f \left(x\right)}{g} \left(x\right)\right] ' = \frac{f ' \left(x\right) g \left(x\right) - f \left(x\right) g ' \left(x\right)}{g} ^ 2 \left(x\right)$

For the given function the derivative is:

$\left[\sin \frac{x}{x} ^ 2\right] ' = \frac{\left(\sin x\right) ' \cdot {x}^{2} - \left({x}^{2}\right) ' \sin x}{x} ^ 4 = \frac{\cos x \cdot {x}^{2} - 2 x \sin x}{x} ^ 4 = \frac{x \cos x - x 2 \sin x}{x} ^ 4 =$

$= \frac{\cos x - 2 \sin x}{x} ^ 3$