How do you differentiate f(x) = (1/3) (arctan(3x))^2?
1 Answer
Jul 30, 2018
Explanation:
"differentiate using the "color(blue)"chain rule"
"given "y=f(g(x))" then"
dy/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"
"noting that "d/dx(arctan(x))=1/(1+x^2)
f'(x)=1/3. 2(arctan(3x))xxd/dx(arctan(3x))
color(white)(f'(x))=2/3arctan(3x). 1/(1+(3x)^2)xxd/dx(3x)
color(white)(f'(x))=(2arctan(3x))/(1+9x^2)
