Q. 3 L5.0( 2 Votes )

# Differentiate the

We need to find derivative of f(x) =

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

f’(x) = {where h is a very small positive number}

derivative of f(x) = is given as –

f’(x) =

f’(x) =

f’(x) =

Taking common, we have –

f’(x) =

Using algebra of limits –

f’(x) =

f’(x) =

As one of the limits can’t be evaluated by directly putting the value of h as it will take 0/0 form.

So we need to take steps to find its value.

As h 0 so, (2hx + h2) 0

multiplying numerator and denominator by (2hx + h2) in order to apply the formula –

f’(x) =

Again using algebra of limits, we have –

f’(x) =

Use the formula:

f’(x) =

f’(x) =

f’(x) =

Hence,

Derivative of f(x) =

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