Question

How do you differentiate `y=1/4arctan(x/4)`?

Answer 1

`dy/dx=1/(16+x^2)`

Explanation:

`•color(white)(x)d/dx(arctanx)=1/(1+x^2)`

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

`"given "y=f(g(x))" then"`

`dy/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"`

`y=1/4arctan(x/4)`

`rArrdy/dx=1/4xx1/(1+(x/4)^2)xxd/dx(x/4)`

`color(white)(rArrdy/dx)=1/4xx1/(1+(x^2/16))xx1/4`

`color(white)(rArrdy/dx)=1/16xx1/(1+(x^2/16))=1/(16+x^2)`