Differentiate each of the following from first principles:

We need to find derivative of f(x) = 1/√(3 – x)


Derivative of a function f(x) from first principle is given by –


{where h is a very small positive number}


derivative of f(x) = 1/√(3 – x) is given as –





Using algebra of limits –




Multiplying numerator and denominator by √(3 – x) + √(3 – x – h) to rationalise the expression so that we don’t get any indeterminate form after putting value of h



Using (a + b)(a – b) = a2 – b2



Using algebra of limits –





Hence,



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