Find the derivative of the function. h(x) = `x^(2)arctan 5x`

1 Answer

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to differentiate the function with respect to x, using product rule and the chaiin rule, such that:

`(u*v) = u'*v + u*v'`

Identifying `u = x^2` and `v = arctan 5x` , yields:

`h'(x) = (x^2)'(arctan 5x) + x^2*(arctan 5x)'`

`h'(x) =2x*arctan 5x + x^2*(1/(1 + (5x)^2))*(5x)'`

`h'(x) =2x*arctan 5x + (5x)^2/(1 + 25x^2)`

Hence, evaluating the deirvative of the given function using product rule and chain rule, yields `h'(x) =2x*arctan 5x + (5x)^2/(1 + 25x^2).`