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Home Differentiation Derivatives of Rational Functions Derivative of 1/v
 
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Derivative of 1/v

For the last two rules in this section we need the formula for the derivative of 1/v.

LEMMA

Suppose v depends on x. Then for any value of x where v ≠ 0 and dv/dx exists,

02_differentiation-123.gif

PROOF

Let y = 1/v and let Δx ≠ 0 be infinitesimal.

02_differentiation-124.gif

Taking standard parts,

02_differentiation-126.gif

Therefore

02_differentiation-127.gif
Home Differentiation Derivatives of Rational Functions Derivative of 1/v

Last Update: 2010-11-25