Front

What is Implicit Differentiation?

Back

A technique used to find the derivative of a function defined implicitly by an equation involving both x and y.

Front

When is Implicit Differentiation used?

Back

It is used when a function is not explicitly solved for y in terms of x.

Front

Differentiate the equation x^3 + y^3 = 36 implicitly with respect to x.

Back

dy/dx = -x^2/y^2.

Front

Differentiate the equation xy + y^2 = 2 implicitly with respect to x.

Back

dy/dx = -y/(x + 2y).

Front

Differentiate the equation xy = 6 implicitly with respect to x.

Back

dy/dx = -y/x.

Front

Differentiate the equation sin(y^2) = x implicitly with respect to x.

Back

dy/dx = 1/(2y cos(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 is the product rule in differentiation?

Back

If u and v are functions of x, then d(uv)/dx = u(dv/dx) + v(du/dx).

Front

How do you apply the product rule in implicit differentiation?

Back

Differentiate both sides of the equation, applying the product rule to terms that are products of functions of x and y.

Front

What is the significance of the derivative dy/dx?

Back

It represents the rate of change of y with respect to x.