Basic Differentiation Rules Flashcards

Questions and Answers

Quid es le resultato de d/dx [cu] secundo le Constant Multiple Rule?

c'u'

cu' (correct)

c'un'

Quid es le resultato de d/dx [u + v] secundo le Addition/Subtraction Rule?

u' + v'

Quid es le resultato de d/dx [uv] secundo le Product Rule?

uv' + u'v

Quid es le resultato de d/dx [u/v] secundo le Quotient Rule?

(uv' - u'v) / v^2 Signup and view all the answers

Quid es le resultato de d/dx [c] secundo le Constant Rule?

0 Signup and view all the answers

Quid es le resultato de d/dx [u^n] secundo le Power Rule?

n(u^(n-1))u' Signup and view all the answers

Quid es le resultato de d/dx [x] secundo le Power Rule?

1 Signup and view all the answers

Quid es le resultato de d/dx [|u|] secundo le Absolute Value Rule?

(u/|u|)u' Signup and view all the answers

Quid es le resultato de d/dx [log{a}(u)] secundo le Logarithm Rule?

u' / ((u)(ln a)) Signup and view all the answers

Quid es le resultato de d/dx [ln u] secundo le Logarithm Rule (Base e)?

u'/u Signup and view all the answers

Quid es le resultato de d/dx [a^u] secundo le Exponential Rule?

(a^u)(ln a)(u') Signup and view all the answers

Quid es le resultato de d/dx [e^u] secundo le Exponential Rule (Base e)?

(e^u)u' Signup and view all the answers

Quid es le resultato de d/dx [sin u] secundo le Sine?

(cos u)(u') Signup and view all the answers

Quid es le resultato de d/dx [cos u] secundo le Cosine?

(-sin u)(u') Signup and view all the answers

Quid es le resultato de d/dx [tan u] secundo le Tangent?

(sec^2 u)(u') Signup and view all the answers

Quid es le resultato de d/dx [cot u] secundo le Cotangent?

(-csc^2 u)(u') Signup and view all the answers

Quid es le resultato de d/dx [sec u] secundo le Secant?

(sec u tan u)(u') Signup and view all the answers

Quid es le resultato de d/dx [csc u] secundo le Cosecant?

(-csc u cot u)(u') Signup and view all the answers

Quid es le resultato de d/dx [arcsin u] secundo le Inverse Sine?

u' / sq rt(1-u^2) Signup and view all the answers

Quid es le resultato de d/dx [arccos u] secundo le Inverse Cosine?

-u' / sq rt(1-u^2) Signup and view all the answers

Quid es le resultato de d/dx [arctan u] secundo le Inverse Tangent?

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

Quid es le resultato de d/dx [arccot u] secundo le Inverse Cotangent?

-u' / (1+u^2) Signup and view all the answers

Quid es le resultato de d/dx [arcsec u] secundo le Inverse Secant?

u' / (|u| sq rt(u^2-1)) Signup and view all the answers

Quid es le resultato de d/dx [arccsc u] secundo le Inverse Cosecant?

-u' / (|u| sq rt(u^2-1)) Signup and view all the answers

Study Notes

Regulas de Differentiation Basic

Regula de Multiplication Constant: Derivata de cu es cu'.
Regula de Addition/Subtraction: Derivata de (u + v) es u' + v'.
Regula de Producto: Derivata de (uv) es uv' + u'v.
Regula de Quotient: Derivata de (u/v) es (uv' - u'v) / v².
Regula de Constant: Derivata de c es 0.
Regula de Potentia: Derivata de (u^n) es n(u^(n-1))u'.
Regula de Potentia pro x: Derivata de x es 1.
Regula de Valor Absoluto: Derivata de |u| es (u/|u|)u'.
Regula de Logarithm: Derivata de logₐ(u) es u' / (u ln a).
Regula de Logarithm (Base e): Derivata de ln u es u'/u.
Regula de Exponential: Derivata de (a^u) es (a^u)(ln a)(u').
Regula de Exponential (Base e): Derivata de e^u es (e^u)u'.

Funções Trigonometricas

Seno: Derivata de sin u es (cos u)(u').
Coseno: Derivata de cos u es (-sin u)(u').
Tangente: Derivata de tan u es (sec² u)(u').
Cotangente: Derivata de cot u es (-csc² u)(u').
Secante: Derivata de sec u es (sec u tan u)(u').
Cosecante: Derivata de csc u es (-csc u cot u)(u').

Funções Inversas

Sine Inverso: Derivata de arcsin u es u' / sqrt(1 - u²).
Coseno Inverso: Derivata de arccos u es -u' / sqrt(1 - u²).
Tangente Inversa: Derivata de arctan u es u' / (1 + u²).
Cotangente Inversa: Derivata de arccot u es -u' / (1 + u²).
Secante Inversa: Derivata de arcsec u es u' / (|u| sqrt(u² - 1)).
Cosecante Inversa: Derivata de arccsc u es -u' / (|u| sqrt(u² - 1)).

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Description

Este quiz adjuva te a memorizar le regulares de differentiatio fundamental. Cataste le regula del constante multiple, addition/subtraction, product, quotient, e power. Similar a un flashcard, iste exercitium es utile pro preparar te pro examina in calculus.