What Is the Multivariable Chain Rule?


Quick Answer

The multivariable chain rule is a formula in calculus used to find the derivative of the composition of multiple functions. In the multivariable chain rule, a function expressed as y(w(x)) can be differentiated using the equation dy/dx = (dy/dw)*(dw/dx), where d indicates the derivative of the variable.

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What Is the Multivariable Chain Rule?
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Full Answer

For example, the equation y = sin(10x) can be solved using the multivariable chain rule by substituting w for 10x. After the substitution, the equation can be written as y(w(x))=sin(w(x)). Using the chain rule to solve this equation results in (dsin(w)/dw) * (dw/dx). The equation can then be further simplified to cos(w)*10 = 10cos(10x).

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