How do you differentiate #f(x) = Tan^(-1) (x/2)#?

1 Answer
Jim G.
Mar 23, 2018

#f'(x)=2/(4+x^2)#

Explanation:

#•color(white)(x)d/dx(tan^-1x)=1/(1+x^2)#

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

#"Given "f(x)=g(h(x))" then"#

#f'(x)=g'(h(x))xxh'(x)larrcolor(blue)"chain rule"#

#f(x)=tan^-1(x/2)#

#rArrf'(x)=1/(1+(x/2)^2)xxd/dx(1/2x)#

#color(white)(rArrf'(x))=(1/2)/(1+x^2/4)xx4/4#

#color(white)(rArrf'(x))=2/(4+x^2)#

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