How do you find the derivative of #u=(6+2x^2)^3#?

2 Answers
sjc
Dec 30, 2017

#(du)/(dx)=12x(6+2x^2)^2#

Explanation:

we will need the chain rule

#(du)/(dx)=color(red)((du)/(dt))color(blue)((dt)/(dx))#

#u=(6+2x^2)^3#

#t=6+2x^2=>color(blue)((dt)/(dx)=4x)#

#u=t^3=>color(red)((du)/(dt)=3t^2)#

#(du)/(dx)=color(red)(3t^2)xxcolor(blue)(4x)#

substitute back and tidy up

#(du)/(dx)=12x(6+2x^2)^2#

Jim G.
Dec 30, 2017

#(du)/dx=12x(6+2x^2)^2#

Explanation:

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

#"given "u=f(g(x)" then"#

#(du)/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"#

#u=(6+2x^2)^3#

#rArr(du)/dx=3(6+2x^2)^2xxd/dx(6+2x^2)#

#color(white)(rArr(du)/dx)=12x(6+2x^2)^2#

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