Question

How do you find the derivative of `y= (5x)/sqrt (x^2+9)`?

Answer 1

`y'=5/sqrt(x^2+9)-(5*x^2)/sqrt(x^2+9)^3`

Explanation:

We Need the product rule

`(uv)'=u'v+uv'`
and the chain rule

`(f(g(x))'=g'(x)*f'(g(x))`
Writing
$$y=5x(x^2+9)^(-1/2)#
so we get

`y'=5(x^2+9)^(-1/2)+5x(-1/2)(x^2+9)^(-3/2)*2x`
this is
`y'=5/sqrt(x^2+9)-(5x^2)/sqrt(x^2+9)^3`