edreshmo.com Cálculo Fórmulas Básicas de Derivación LA DERIVADA ∀ u = f(x) , ∀ v = g(x) , ∀ c , e , n ∈ ℝ , a ∈ ℝ+ − {1} , e = 2.7182818284 5904523536 0287471352 … 1. d (c) = 0 dx 13. d 1 d (u) (ln(u)) = dx u dx 2. d (x) = 1 dx 14. d d cos(u) = −sen(u) (u) dx dx 3. d d (cu) = c (u) dx dx 15. d d tan(u) = sec2 (u) (u) dx dx 4. d d d (u ± v) = (u) ± (v) dx dx dx 16. d d cot(u) = −csc2 (u) (u) dx dx 5. d d d (uv) = u (v) + v (u) dx dx dx 17. d d sec(u) = sec(u)tan(u) (u) dx dx d d v (u) − u (v) d u dx dx 6. ( )= dx v v2 18. d d csc(u) = −csc(u)cot(u) (u) dx dx 19. d 1 d (u) arcsen(u) = dx √1 − u2 dx d n d (u ) = nun−1 (u) 7. dx dx 8. d v d d (u ) = vuv−1 (u) + uv ln(u) (v) dx dx dx 20. d −1 d (u) arccos(u) = 2 dx dx √1 − u 9. d u d (a ) = au ln(a) (u) dx dx 21. d 1 d (u) arctan(u) = dx 1 + u2 dx 10. d u d (e ) = eu (u) dx dx 22. d −1 d (u) arccot(u) = dx 1 + u2 dx 11. d u d (|u|) = (u) |u| dx dx 23. d 1 d (u) arcsec(u) = 2 dx dx u √u − 1 12. d 1 d (u) (loga (u)) = dx u ln(a) dx 24. d -1 d (u) arccsc(u) = 2 dx dx u √u -1 Regla de la Cadena d d d (y) = (y) (u) dx du dx Definición de Derivada de una Función d f(x + ∆x) − f(x) (y) = lím ∆x→0 dx ∆x Notaciones de la Derivada d d ' (y) = f(x) = y' = f (x) = Dx y dx dx formulasdematematica.com