Derivatives and Integrals in Calculus

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?

sec x tan x Signup and view all the answers

Qual è le derivata de csc x?

-csc x cot x Signup and view all the answers

Qual è le derivata de cot x?

-csc^2 x Signup and view all the answers

Qual è le derivata de arcsin x?

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

Qual è le derivata de arccos x?

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

Qual è le derivata de arctan x?

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

Qual è le derivata de a^x?

a^x ln(a) Signup and view all the answers

Qual è le derivata de e^x?

e^x Signup and view all the answers

Qual è le derivata de ln(x)?

1/x Signup and view all the answers

Qual è le integral de cos u?

sin u Signup and view all the answers

Qual è le integral de sin u?

-cos u Signup and view all the answers

Qual è le integral de sec^2 u?

tan u Signup and view all the answers

Qual è le integral de sec u tan u?

sec u Signup and view all the answers

Qual è le integral de csc u cot u?

-csc u Signup and view all the answers

Qual è le integral de csc^2 u?

-cot u Signup and view all the answers

Qual è le integral de tan u?

ln|sec u| Signup and view all the answers

Qual è le integral de sec u?

ln|sec u + tan u| Signup and view all the answers

Qual è le integral de 1/(a^2+x^2)?

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

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

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

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

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

Qual è le integral de a^kx?

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

Qual è le integral de cot x?

ln|sin x| Signup and view all the answers

Qual è le integral de csc x?

-ln|sec x + tan x| Signup and view all the answers

Qual è le forma de sin^2 x?

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

Qual è le forma de cos^2 x?

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

Sin^2 x + cos^2 x = ?

1 Signup and view all the answers

1 + cot^2 x = ?

csc^2 x Signup and view all the answers

1 + tan^2 x = ?

sec^2 x 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.

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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.