`y = 3(x^2)sec(x)` Use the Product Rule or the Quotient Rule to find the derivative of the function.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to evaluate the derivative of the given function, using the product tule for the product  `3x^2*sec x` , such that:

`f'(x) = (3x^2)'*(sec x) + 3x^2*(sec x)'`

`f'(x) = 6x*(sec x)+ 3x^2*(sec x)*(tan x) `

Factoring out `3x*sec x` yields:

`f'(x) = 3x*sec x*(2 + x*tan x)`

Hence, evaluating the derivative of the function, using the product rule where it is requested, yields `f'(x) = 3x*sec x*(2 + x*tan x).`