IMPLICITE DIFF

Front

What is implicit differentiation?

Back

Implicit differentiation is a technique used to find the derivative of a function that is not explicitly solved for one variable in terms of another.

Front

How do you find dy/dx using implicit differentiation?

Back

To find dy/dx using 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 does the derivative represent in calculus?

Back

The derivative represents the slope of the tangent line to the curve at a given point.

Front

What is the formula for the derivative of y with respect to x in the equation 2x^2 - 3y^2 = 4?

Back

The formula is dy/dx = 2x / (3y).

Front

How do you find dy/dx at a specific point?

Back

To find dy/dx at a specific point, first find the derivative using implicit differentiation, then substitute the coordinates of the point into the derivative.

Front

What is the derivative of the equation 3x^2 - 5x + 6y^2 - 7y = 24?

Back

The derivative is dy/dx = (-6x + 5) / (12y - 7).

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 significance of the slope of the tangent line?

Back

The slope of the tangent line indicates the rate of change of the function at that specific point.

Front

What is the relationship between x and y in implicit differentiation?

Back

In implicit differentiation, y is treated as a function of x, meaning y can change as x changes.

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.