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

1 Answer
Sonnhard
Jul 11, 2018

#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#

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