Homework SourseFind the derivative of fx arctanx9 fx Solution You use the
Find the derivative of f(x) = arctan(x^9)
f\'(x)= ???
f\'(x)= ???
Solution
You use the chain-rule here g(h(x))\' = g\'(h(x))h\'(x) I use g(h(x)) rather than f(g(x)) because the function given is f(x) In this case, as f(x) = arctan(x^9), g(x) = arctan(x) and h(x) = x^9 The derivative of [g(x) = arctan(x)] = 1/(1+x^2) Thus, g\'(h(x)) = 1/(1+h(x)^2) = 1/(1+(x^9)^2) = 1/(1+x^18) As h(x) = x^9), h\'(x) = 9x^8 Thus, f\'(x) = g\'(h(x))h\'(x) = 1/(1+x^18) * 9x^8 or 9x^8/(1+x^18)
