How do you use the chain rule to differentiate #y=4(x^3+5)^(3/4)#?

1 Answer
Jim G.
Jul 29, 2016

#dy/dx=(9x^2)/((x^3+5)^(1/4))#

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)|)))........ (A)#

let #color(blue)(u=x^3+5)rArr(du)/dx=3x^2#

and #y=4color(blue)(u)^(3/4)rArr(dy)/(du)=3color(blue)(u)^(-1/4)#

substitute these values into (A) and convert u to x

#rArrdy/dx=3color(blue)(u)^(-1/4).3x^2=(9x^2)/(x^3+5)^(1/4)#

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