How do you differentiate #y=tan^-1(2x^4)#?
1 Answer
Dec 8, 2016
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)#