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functions of stochastic processes

Ito’s lemma, otherwise known as the Ito formula, expresses functions of stochastic processes in terms of stochastic integrals.

by subtraction Denoting the risk-free interest rate and the dividend yield by and respectively

Ito's lemma implies so by subtraction Denoting the risk-free interest rate and the dividend yield by and respectively, trading in a cash account a risk-neutral world the first term is equal to.

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the mathematical tool we can use to prove that a potential solution to our SDE really satisfies the SDE

Ito's Lemma is the mathematical tool we can use to prove that a potential solution to our SDE really satisfies the SDE.

otherwise known as the Ito formula

Ito’s lemma, otherwise known as the Ito formula, expresses functions of stochastic processes in terms of stochastic integrals.

a fundamental result in Ito calculus

The Ito lemma is a fundamental result in Ito calculus.

the stochastic version of the chain rule of standard calculus

To answer the more general question that seems to be giving you trouble, Ito's lemma is the stochastic version of the chain rule of standard calculus.

a stochastic analogue of the chain rule of ordinary calculus

Ito's Lemma is a stochastic analogue of the chain rule of ordinary calculus.

used to determine the derivative of a time-dependent function of a stochastic process

Ito's Lemma is a key component in the Ito Calculus, used to determine the derivative of a time-dependent function of a stochastic process.

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a key component in the Ito Calculus

Ito's Lemma is a key component in the Ito Calculus, used to determine the derivative of a time-dependent function of a stochastic process.

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a cornerstone of quantitative finance and quantitative finance

Ito's Lemma is a cornerstone of quantitative finance and quantitative finance is intrinsic to the derivation of the Black-Scholes equation for contingent claims (options) pricing.

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