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

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to find d/dx[x^2*f(x)] for x=2 and where f'(2) = 3

y = x^2*f(x)

use the product rule

y' = [x^2*f(x)]'

=> y' = (x^2)'*f(x) + x^2*f'(x)

=> y' = 2x*f(x) + x^2*f'(x)

As f'(2) = 3

At x = 2, y' = 2*2*f(x) + 2^2*3

=> y' = 4*f(x) + 12

As f(x) is not given we cannot solve this further.

The required derivative is 4*f(x) + 12

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