Step 1: Insert the function into the formula. The function is √(4x + 1), so:
f'(x) = lim _{Δx → 0} √( 4( x + Δx ) + 1 – √(4x + 1) ) / Δx.
If this looks confusing, all we’ve done is changed “x” in the formula to x + Δx in the first part of the formula.

• Derivative of a constant function is always equal to zero because there is nothing which is going to change in it with respect to any other variable!
• But, if a constant is multiplied by some function, say ‘ f ’ then we just take it out of the differentiation and we get the derivative as, constant × (f’), e.g. differentiation of  2x² is 4x and that of 3x³ will be 9x².
• You will notice here that along with Differentiation Rules and Formulas, we must keep in mind, which type of function we are differentiating and ‘with respect to’ (w.r.t.) what function/variable. Because, that actually changes the flow of differentiation and we get the derivative accordingly.

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