Implicit Differentiation

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

What is the first step in Implicit Differentiation?

Back

Differentiate both sides of the equation with respect to x, applying the chain rule to terms involving y.

Front

What does dy/dx represent?

Back

The derivative of y with respect to x, indicating the rate of change of y as x changes.

Front

How do you differentiate y with respect to x?

Back

When differentiating y, treat it as a function of x and multiply by dy/dx.

Front

What is the derivative of a constant?

Back

The derivative of a constant is zero.

Front

If y is a function of x, what is the derivative of x^n?

Back

The derivative is n*x^(n-1), where n is a constant.

Front

How do you isolate dy/dx after implicit differentiation?

Back

Rearrange the equation to solve for dy/dx after differentiating both sides.

Front

What is the derivative of y^n with respect to x?

Back

The derivative is n*y^(n-1) * dy/dx.

Front

What is the implicit differentiation of the equation 9y + x = 4y?

Back

dy/dx = -1/5.