d d dx dx (ten terms) = ... + (ten terms) = . We note that this limit may be evaluated using product rule too. Write f ( x ) = x = uv , where u is the constant function taking value everywhere and v ( x ) = x .
Here, f ( x ) = x = uv we know that the derivative of u equals . Also derivative of v ( x ) = x equals . Thus by the product rule we have f ′