How do you differentiate #y=tan^-1(2x^4)#?

1 Answer
Dec 8, 2016

#dy/dx=(8x^3)/(1+4x^8)#

Explanation:

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx(tan^-1x)=1/(1+x^2))color(white)(2/2)|)))#

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

#color(red)(bar(ul(|color(white)(2/2)color(black)(dy/dx=(dy)/(du)xx(du)/(dx))color(white)(2/2)|)))to(A)#

#"let " u=2x^4rArr(du)/(dx)=8x^3#

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

Substitute into (A) and change u back to x

#dy/dx=1/(1+u^2)xx8x^3=(8x^3)/(1+4x^8)#