Find dy/dx if $$3x^2 - 5x + 6y^2 - 7y = 24$$ .

$$\frac{dy}{dx} = \frac{-6x + 5}{12y - 7}$$ .

Find dy/dx if $$4x + 12y = 10$$ .

$$\frac{dy}{dx} = -\frac{1}{3}$$ .

Find dy/dx by Implicit Differentiation for $$x^3 + y^3 = 36$$ .

$$\frac{dy}{dx} = -\frac{x^2}{y^2}$$ .

Find $$\frac{dy}{dx}$$ for $$y^2 = 10x$$ .

$$\frac{dy}{dx} = \frac{5}{y}$$ .

What is the Chain Rule in differentiation?

The Chain Rule states that if a function y is composed of another function u, then the derivative of y with respect to x is given by: $$\frac{dy}{dx} = \frac{dy}{du} \frac{du}{dx}$$ .

What is the Quotient Rule in differentiation?

The Quotient Rule states that if you have two functions f(x) and g(x), the derivative of their quotient is given by: $$\frac{d}{dx}igg(\frac{f}{g}igg) = \frac{f$$ .

What is the significance of the derivative in calculus?

The derivative represents the rate of change of a function with respect to its variable. It provides information about the slope of the tangent line to the curve at any point.

How do you apply the Chain Rule in implicit differentiation?

When differentiating terms involving y in implicit differentiation, apply the Chain Rule by multiplying the derivative of the outer function by the derivative of the inner function, which is $$\frac{dy}{dx}$$ .

What is the relationship between implicit differentiation and solving for y?

Implicit differentiation allows us to find the derivative $$\frac{dy}{dx}$$ without explicitly solving for y in terms of x, which can be useful for complex equations.

What is an example of an equation suitable for implicit differentiation?

An example of an equation suitable for implicit differentiation is $$x^2 + y^2 = 1$$ , which represents a circle.

What is the first step in implicit differentiation?

The first step in implicit differentiation is to differentiate both sides of the equation with respect to x, treating y as a function of x.

Implicit Differentiation Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is Implicit Differentiation?

Back

Implicit differentiation is a technique used to differentiate equations where the dependent and independent variables are not separated. It involves differentiating both sides of an equation with respect to the independent variable and then solving for the derivative of the dependent variable.

2.

FLASHCARD QUESTION

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, applying the chain rule when differentiating terms involving y. Then, solve for dy/dx.

3.

FLASHCARD QUESTION

Front

What is the derivative of y^2 with respect to x?

Back

4.

FLASHCARD QUESTION

Front

What is the Product Rule in differentiation?

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

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Back

7.

FLASHCARD QUESTION

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