Derivatives and Integrals in Calculus
31 Questions
102 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

Qual è le derivata de sin x?

cos x

Qual è le derivata de cos x?

-sin x

Qual è le derivata de tan x?

sec^2 x

Qual è le derivata de sec x?

<p>sec x tan x</p> Signup and view all the answers

Qual è le derivata de csc x?

<p>-csc x cot x</p> Signup and view all the answers

Qual è le derivata de cot x?

<p>-csc^2 x</p> Signup and view all the answers

Qual è le derivata de arcsin x?

<p>1/square root of 1-x^2</p> Signup and view all the answers

Qual è le derivata de arccos x?

<p>-1/square root of 1-x^2</p> Signup and view all the answers

Qual è le derivata de arctan x?

<p>1/(1+x^2)</p> Signup and view all the answers

Qual è le derivata de a^x?

<p>a^x ln(a)</p> Signup and view all the answers

Qual è le derivata de e^x?

<p>e^x</p> Signup and view all the answers

Qual è le derivata de ln(x)?

<p>1/x</p> Signup and view all the answers

Qual è le integral de cos u?

<p>sin u</p> Signup and view all the answers

Qual è le integral de sin u?

<p>-cos u</p> Signup and view all the answers

Qual è le integral de sec^2 u?

<p>tan u</p> Signup and view all the answers

Qual è le integral de sec u tan u?

<p>sec u</p> Signup and view all the answers

Qual è le integral de csc u cot u?

<p>-csc u</p> Signup and view all the answers

Qual è le integral de csc^2 u?

<p>-cot u</p> Signup and view all the answers

Qual è le integral de tan u?

<p>ln|sec u|</p> Signup and view all the answers

Qual è le integral de sec u?

<p>ln|sec u + tan u|</p> Signup and view all the answers

Qual è le integral de 1/(a^2+x^2)?

<p>1/a arctan(x/a)</p> Signup and view all the answers

Qual è le integral de 1/square root of (a^2 - x^2)?

<p>arcsin(x/a)</p> Signup and view all the answers

Qual è le integral de 1/(x times square root of (x^2 - a^2))?

<p>1/a arcsec(x/a)</p> Signup and view all the answers

Qual è le integral de a^kx?

<p>(1/(k lna)) a^kx</p> Signup and view all the answers

Qual è le integral de cot x?

<p>ln|sin x|</p> Signup and view all the answers

Qual è le integral de csc x?

<p>-ln|sec x + tan x|</p> Signup and view all the answers

Qual è le forma de sin^2 x?

<p>(1-cos(2x))/2</p> Signup and view all the answers

Qual è le forma de cos^2 x?

<p>(1 + cos(2x))/2</p> Signup and view all the answers

Sin^2 x + cos^2 x = ?

<p>1</p> Signup and view all the answers

1 + cot^2 x = ?

<p>csc^2 x</p> Signup and view all the answers

1 + tan^2 x = ?

<p>sec^2 x</p> Signup and view all the answers

Study Notes

Derivatives of Trigonometric Functions

  • Derivative of sin x es cos x.
  • Derivative de cos x es -sin x.
  • Derivative de tan x es sec^2 x.
  • Derivative de sec x es sec x tan x.
  • Derivative de csc x es -csc x cot x.
  • Derivative de cot x es -csc^2 x.

Derivatives of Inverse Trigonometric Functions

  • Derivative de arcsin x es 1/square root de (1-x^2).
  • Derivative de arccos x es -1/square root de (1-x^2).
  • Derivative de arctan x es 1/(1+x^2).

Derivatives of Exponential and Logarithmic Functions

  • Derivative de a^x es a^x ln(a).
  • Derivative de e^x es e^x.
  • Derivative de ln(x) es 1/x.

Integrals of Trigonometric Functions

  • Integral de cos u es sin u.
  • Integral de sin u es -cos u.
  • Integral de sec^2 u es tan u.
  • Integral de sec u tan u es sec u.
  • Integral de csc u cot u es -csc u.
  • Integral de csc^2 u es -cot u.

Integrals of Special Functions

  • Integral de tan u es ln|sec u|.
  • Integral de sec u es ln|sec u + tan u|.

Integrals of Rational Functions

  • Integral de 1/(a^2+x^2) es (1/a) arctan (x/a).
  • Integral de 1/square root de (a^2 - x^2) es arcsin (x/a).
  • Integral de 1/(x * square root de (x^2-a^2)) es (1/a) arcsec (x/a).

Integrals of Power Functions

  • Integral de a^kx es (1/(k ln(a))) a^kx.

Additional Integrals and Identities

  • Integral de cot x es ln|sin x|.
  • Integral de csc x es -ln|sec x + tan x|.
  • Relation sin^2 x es (1 - cos(2x))/2.
  • Relation cos^2 x es (1 + cos(2x))/2.
  • Identidad sin^2 x + cos^2 x es 1.
  • Identidad 1 + cot^2 x es csc^2 x.
  • Identidad 1 + tan^2 x es sec^2 x.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

Description

Este quiz tracta del derivadas e integrales de functiones trigonometric, exponentiales e logarithmicas. Es importante comprender los conceptos e formulas fundamentales para resolver problemas de calculo. Practica a tu nivel de comprehension con este cuestionario.

More Like This

Use Quizgecko on...
Browser
Open
Browser
Browser