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

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stevenbawi103 | Student, College Sophomore | eNoter

Posted February 25, 2013 at 5:45 PM via web

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Find the derivative of the function.

h(x) = `x^(2)arctan 5x`

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted February 25, 2013 at 5:59 PM (Answer #1)

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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).`

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