Implicit Differentiation

Front

What is implicit differentiation?

Back

Implicit differentiation is a technique used to differentiate equations that define y implicitly in terms of x, rather than explicitly as y = f(x).

Front

How do you apply implicit differentiation to an equation?

Back

To apply implicit differentiation, differentiate both sides of the equation with respect to x, treating y as a function of x, and then solve for dy/dx.

Front

What is the derivative of y with respect to x when using implicit differentiation?

Back

The derivative of y with respect to x is denoted as dy/dx.

Front

What is the first step in implicit differentiation?

Back

The first step is to differentiate both sides of the equation with respect to x.

Front

When differentiating y^n, what do you need to include?

Back

When differentiating y^n, you need to include the chain rule, resulting in n*y^(n-1)*dy/dx.

Front

What is the implicit differentiation of the equation x + 4y = 1?

Back

The implicit differentiation of the equation x + 4y = 1 gives dy/dx = -1/4.

Front

How do you find dy/dx for the equation 2x^2 - 3y^2 = 4?

Back

Differentiate both sides to get 4x - 6y(dy/dx) = 0, then solve for dy/dx to find dy/dx = 2x/(3y).

Front

What is the result of implicit differentiation for the equation x^3 + y^3 = 36?

Back

The result is dy/dx = -x^2/y^2.

Front

What is the chain rule in the context of implicit differentiation?

Back

The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

Front

What does it mean for y to be an implicit function of x?

Back

It means that y is defined in terms of x through an equation, but y is not isolated on one side of the equation.