# How do you differentiate #f(x)=1/sqrt(x-3x^3+5x^5# using the quotient rule?

We use The Chain Rule in these situations, which stipulates that,

Taken together,

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To differentiate ( f(x) = \frac{1}{\sqrt{x-3x^3+5x^5}} ) using the quotient rule, first, identify ( u ) and ( v ) as follows:

( u = 1 )

( v = \sqrt{x-3x^3+5x^5} )

Then, apply the quotient rule formula:

[ f'(x) = \frac{u'v - uv'}{v^2} ]

Where:

( u' = 0 )

( v' = \frac{1}{2\sqrt{x-3x^3+5x^5}} \cdot (1 - 9x^2 + 25x^4) )

After substituting these values into the quotient rule formula, simplify to get the derivative of ( f(x) ).

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