What is the 13th derivative of $$y=9\text{sin}(x)$$ ?

$$f^{13}(x)=9\text{sin}(x)$$ (since the sine function has a period of 4 derivatives)

What is the 2nd derivative of $$y=\frac{3}{x^2}-\frac{12}{x^3}+\frac{11}{x^4}-\frac{8}{12}$$ ?

$$\frac{d^2y}{dx^2}=\frac{18}{x^4}-\frac{144}{x^5}+\frac{220}{x^6}$$

What is the 3rd derivative of $$y=\frac{3}{x^2}-\frac{12}{x^3}+\frac{11}{x^4}-\frac{8}{12}$$ ?

$$\frac{d^3y}{dx^3}=-\frac{72}{x^5}+\frac{720}{x^6}-\frac{1320}{x^7}$$

What is the general formula for the nth derivative of $$y=\text{sin}(x)$$ ?

The nth derivative of $$y=\text{sin}(x)$$ cycles through $$\text{sin}(x), \text{cos}(x), -\text{sin}(x), -\text{cos}(x)$$ .

What is the power rule for differentiation?

If $$y=x^n$$ , then $$\frac{dy}{dx}=nx^{n-1}$$ .

How do you find the derivative of a function at a point?

Use the limit definition: $$f$$ as $$h \to 0$$ .

What is the relationship between the first and second derivatives?

The first derivative gives the slope of the function, while the second derivative gives the concavity.

What is the significance of the second derivative test?

It helps determine the local maxima and minima of a function based on the sign of the second derivative.

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

$$\frac{dy}{dx}=-\text{sin}(x)$$ .

What is the formula for the nth derivative of $$y=e^x$$ ?

The nth derivative of $$y=e^x$$ is $$\frac{d^n}{dx^n}e^x=e^x$$ .

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

$$\frac{dy}{dx}=\text{sec}^2(x)$$ .

What is the formula for the derivative of a quotient?

If $$y=\frac{u}{v}$$ , then $$\frac{dy}{dx}=\frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^2}$$ .

Review 3 for FINAL Higher Order Derivatives& EQUATION OF TANGENT Flashcards

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FLASHCARD QUESTION

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2.

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3.

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4.

FLASHCARD QUESTION

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What is the formula for finding the nth derivative of a polynomial function?

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5.

FLASHCARD QUESTION

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What is the equation of the tangent line to a function at a given point?

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