What is the derivative of $$f^{-1}(b)$$ given that $$f(a) = b$$ ?

The derivative is given by the formula: $$\frac{d}{dx}[f^{-1}(b)] = \frac{1}{\frac{d}{dx}[f^{-1}(a)]}$$ .

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

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

What is the derivative of $$x$$ ?

The derivative of $$x$$ is $$1$$ .

What is the derivative of $$cx$$ where $$c$$ is a constant?

The derivative of $$cx$$ is $$c$$ .

What is the derivative of $$\text{arccot}(x)$$ ?

The derivative of $$\text{arccot}(x)$$ is $$-\frac{1}{1+x^2}$$ .

What is the Chain Rule in differentiation?

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

What is the Product Rule for differentiation?

The Product Rule states that if $$u(x)$$ and $$v(x)$$ are functions, then $$\frac{d}{dx}[u(x)v(x)] = u$$ .

What is the Quotient Rule for differentiation?

The Quotient Rule states that if $$u(x)$$ and $$v(x)$$ are functions, then $$\frac{d}{dx}igg[\frac{u(x)}{v(x)}igg] = \frac{u$$ .

What is the derivative of $$\frac{1}{x}$$ ?

The derivative of $$\frac{1}{x}$$ is $$-\frac{1}{x^2}$$ .

What is the derivative of $$\text{sin}(x)$$ ?

The derivative of $$\text{sin}(x)$$ is $$\text{cos}(x)$$ .

What is the derivative of $$\text{cos}(x)$$ ?

The derivative of $$\text{cos}(x)$$ is $$-\text{sin}(x)$$ .

What is the derivative of $$\text{tan}(x)$$ ?

The derivative of $$\text{tan}(x)$$ is $$\text{sec}^2(x)$$ .

What is the derivative of $$\text{ln}(x)$$ ?

The derivative of $$\text{ln}(x)$$ is $$\frac{1}{x}$$ .

AP Calculus - Derivative Definition & Rules Flashcards

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1.

FLASHCARD QUESTION

Front

Define the derivative of a function at a point.

Back

The derivative of a function at a point is the limit of the average rate of change of the function as the interval approaches zero. It represents the slope of the tangent line to the function at that point.

2.

FLASHCARD QUESTION

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