Find $$\frac{dy}{dx}$$ for $$2x^2+xy+3y^2=0$$

$$\frac{-\left(4x+y\right)}{x+6y}$$

The set of all critical numbers of $$f(x)=\left(x^2-x-2\right)^{\frac{1}{3}}$$ equals

$$\left\{-1,\ \frac{1}{2},\ 2\right\}$$

How to find the derivative of $$y=5\cos x-3\sin x+4x$$ ?

Use the sum rule and differentiate each term: $$\frac{dy}{dx} = -5\sin x - 3\cos x + 4$$ .

What is the formula for the second derivative?

The second derivative, $$\frac{d^2y}{dx^2}$$ , measures the rate of change of the first derivative.

What does $$\frac{dy}{dx}$$ represent?

The derivative of y with respect to x, indicating the slope of the tangent line to the curve at a point.

How to find critical numbers of a function?

Set the first derivative equal to zero and solve for x.

What is the relationship between position, velocity, and acceleration?

Velocity is the derivative of position, and acceleration is the derivative of velocity.

What is the product rule in differentiation?

If $$u(x)$$ and $$v(x)$$ are functions, then $$\frac{d}{dx}[u(x)v(x)] = u$$ .

What is the chain rule in differentiation?

If $$y = f(g(x))$$ , then $$\frac{dy}{dx} = f$$ .

How to apply implicit differentiation to $$x^3+y^3=36$$ ?

Differentiate both sides with respect to x, treating y as a function of x, and solve for $$\frac{dy}{dx}$$ .

Final Exam Review (Units 1-5) Flashcards

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1.

FLASHCARD QUESTION

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2.

FLASHCARD QUESTION

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3.

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4.

FLASHCARD QUESTION

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5.

FLASHCARD QUESTION

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264 ft/sec

6.

FLASHCARD QUESTION

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Definition of Implicit Differentiation

Back

A technique used to differentiate equations where y is not isolated on one side.

7.

FLASHCARD QUESTION

Front

What is a critical number?

Back

A value of x where the derivative is zero or undefined, indicating potential local maxima or minima.

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