Calculate d/dx(x^2f(x)) for x=2 and f '(2)=3  

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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`d/dx (x^2 f(x)) ==> f'(2)= 3`

`d/dx (x^2 f(x))= (x^2)f'(x) + (x^2)' f(x).`

`==> d/dx (x^2 f(x))= x^2 f'(x) + 2x f(x).`

``

`` Now when x= 2.

==> `d/dx (4f(2)) = 2^2 f'(2) + 2*2*f(2)`

`==> d/dx (4f(2)) = 4*3 + 4f(2)`

`==> d/dx (4f(2)) = 12 + 4f(2)`

`` =`==> d/dx (x^2 f(x)) = 12 + 4f(2).`   as x= 2.

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