How to take the derivative of an equation implicitly

The video tutorial explains the process of differentiating an equation with respect to X. It begins by introducing the concept of differentiation and applying derivatives to various terms. The instructor then simplifies the equation by combining like terms and factoring out common elements. The main goal is to solve for DY DX, which is achieved by isolating DY DX on one side of the equation and dividing by the remaining terms. The final solution is presented as DY DX equals 2X over three y squared plus 2Y minus 5.

What is the first step in differentiating an equation with respect to X?

• Solve for the constant term.

• Factor out common terms.

• Combine all terms on one side.

• Apply the derivative operator to each term.

When simplifying the differentiated equation, what should you do with terms that contain dy/dx?

• Move them to the right side of the equation.

• Combine them with like terms.

• Ignore them.

• Factor them out.

What is the purpose of factoring out dy/dx in the equation?

• To make the equation more complex.

• To isolate dy/dx for solving.

• To simplify the equation by combining like terms.

• To eliminate dy/dx from the equation.

How do you solve for dy/dx after factoring it out?

• Subtract the constant term.

• Divide by the expression that was factored out.

• Multiply by the reciprocal of the remaining expression.

• Add all terms to one side.

What is the final expression for dy/dx in the given problem?

• dy/dx = 3y^2 + 2Y - 5

• dy/dx = 3y^2 + 2Y - 5 over 2X

• dy/dx = 2X + 3y^2 + 2Y - 5

• dy/dx = 2X over 3y^2 + 2Y - 5