Q:

# What is the multivariable chain rule?

A:

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.

## Keep Learning

Credit: VikramRaghuvanshi E+ Getty Images

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).

Sources:

## Related Questions

• A: In calculus, the primary significance of 1/x is its value as the derivative of the natural logarithm of "x." The proof for the derivative of ln(x) may be f... Full Answer >
Filed Under:
• A: The midpoint rule of calculus is a method for approximating the value of the area under the graph during numerical integration. This is one of several rule... Full Answer >
Filed Under:
• A: In calculus, critical points or stationary points are any values of differentiable functions of complex or real variables whose derivative is 0, f(x0) = 0.... Full Answer >
Filed Under:
• A: Single variable calculus covers derivative and integral functions that contain one variable. Functions that contain two or more variables are a part of mul... Full Answer >
Filed Under:
PEOPLE SEARCH FOR