How do you use the chain rule to differentiate #y=(x^2+4x)^(1/2)#?

1 Answer
Jim G.
Aug 6, 2016

#dy/dx=(x+2)/(x^+4x)^(1/2)#

Explanation:

differentiate using the #color(blue)"chain rule"#

#color(red)(|bar(ul(color(white)(a/a)color(black)(dy/dx=(dy)/(du)xx(du)/(dx))color(white)(a/a)|)))#

let #u=x^2+4xrArr(du)/(dx)=2x+4=2(x+2)#

and #y=u^(1/2)rArr(dy)/(du)=1/2u^(-1/2)#

#rArrdy/dx=1/2u^(-1/2).2(x+2)#

and convert u back into terms of x

#rArrdy/dx=(x+2)/(x^2+4x)^(1/2)#

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