What does $$f$$ represent?

$$f$$ represents the derivative of the function f at the point x, indicating the rate of change of f with respect to x.

What is the derivative of $$x$$ ?

The derivative of $$x$$ is 1, as it represents a constant rate of change.

What is the derivative of $$x^2$$ ?

The derivative of $$x^2$$ is $$2x$$ .

What is the product rule for differentiation?

The product rule states that if $$u(x)$$ and $$v(x)$$ are functions, then the derivative of their product is $$(uv)$$ .

What is the quotient rule for differentiation?

The quotient rule states that if $$u(x)$$ and $$v(x)$$ are functions, then the derivative of their quotient is $$\frac{u}{v}$$ .

What is the chain rule for differentiation?

The chain rule states that if $$y = f(g(x))$$ , then the derivative is $$\frac{dy}{dx} = f$$ .

What is the significance of the slope of the tangent line?

The slope of the tangent line at a point on a curve represents the instantaneous rate of change of the function at that point.

What is the relationship between derivatives and motion?

In motion, the derivative of the position function with respect to time gives the velocity, and the derivative of the velocity function gives the acceleration.

What is the second derivative?

The second derivative, denoted as $$f$$ , is the derivative of the derivative of a function, indicating the rate of change of the rate of change.

What does it mean if the second derivative is positive?

If the second derivative is positive, it indicates that the function is concave up, meaning the slope of the tangent line is increasing.

What does it mean if the second derivative is negative?

If the second derivative is negative, it indicates that the function is concave down, meaning the slope of the tangent line is decreasing.

Formative Differentiation basics

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the definition of a derivative?

Back

The derivative of a function at a point is the slope of the tangent line to the graph of the function at that point. It represents the rate of change of the function with respect to its variable.

2.

FLASHCARD QUESTION

Front

What is the formula for the derivative of a function f(x)?

Back

3.

FLASHCARD QUESTION

Front

Back

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