Question

LA DERIVADA DE Y= X AL CUADRADO + 2X

Answer 1

1.1. Derivadas directas 1. f(x) = x 2 + x + 1 R. f ′ (x) = 2x + 1. 2. f(x) = x a + x R. f ′ (x) = axa−1 + 1. 3. f(x) = (x 2 + x)(x) R. f ′ (x) = 3x 2 + 2x. 4. f(x) = (x + 1)(x + 2) R. f ′ (x) = 2x + 3. 5. f(x) = (x 2 − 1)(x 3 + 2) R. f ′ (x) = 5x 4 − 3x 2 + 4x. 6. f(x) = (x 2 + x + 1)(x 3 − 2x + 3) R. f ′ (x) = 5x 4 + 4x 3 − 3x 2 + 2x + 1. 7. f(x) = sin2 (x) R. f ′ (x) = sin(2x). 8. f(x) = x cos(x) R. f ′ (x) = cos x − x sin x. 9. f(x) = (√ x)(x 2 + 3) R. f ′ (x) = 3 + 5x 2 2 √ x . 10. f(x) = √3 x 2 + a R. f ′ (x) = 2x 3(a + x 2) (2/3). 11. f(x) = a √ x + a R. f ′ (x) = a 2 √ a + x . 12. f(x) = (a 2 − x 2 ) √ x 2 + a 2 R. f ′ (x) = − x(a 2 + 3x 2 ) √ a 2 + x 2 . 13. f(x) = √ x 2 + b 2 √ x 2 + a 2 R. f ′ (x) = x(a 2 + b 2 + 2x 2 ) √ a 2 + x 2 √ b 2 + x 2 . 14. f(x) = (√ x + 1)(√ x − 2) R. f ′ (x) = 1 − 1 2 √ x . 15. f(x) = (√ x + x)(√ x − x) R. f ′ (x) = 1 − 2x. 1.1. DERIVADAS DIRECTAS 16. f ( x) = ( √ x + x ) / ( √ x − x ) R. f ′ ( x) = 1 ( √ x − 1) 2 √ x . 17. f ( x) = 1 / ( √ x + 1) R. f ′ ( x) = 1 2( √ x + 1) 2 √ x . 18. f ( x) = ( √ x + 1) / ( x 2 − x ) R. f ′ ( x) = 2 − 3 √ x 2( √ x − 1) 2 x 2 . 19. f ( x) = x/ sin x R. f ′ ( x) = (1 − x cot x)(csc( x)) . 20. f ( x) = sin x 1 − cos x R. f ′ ( x) = 1 cos x − 1 . 21. f ( x) = sin x(sin x + cos x ) R. f ′ ( x) = cos 2 x + sin2 x . 22. f ( x) = sec x x R. f ′ ( x) = sec x ( x tan x − 1) x 2 . 23. f ( x) = x 1 − sin x R. f ′ ( x) = 1 + x cos x − sin x (sin x − 1) 2 . 24. f ( x) = x a + bx 2 R. f ′ ( x) = a − bx 2 ( a + bx 2 ) 2 . 25. f ( x) = 1 / √ x R. f ′ ( x) = − 1 2 x √ x . 26. f ( x) = x/ √ x R. f ′ ( x) = 1 2 √ x . 27. f ( x) = 1 / √ x + 1 R. f ′ ( x) = − 1 2(1 + x ) 3 / 2 . 28. f ( x) = x/ √ x 2 + 1 R. f ′ ( x) = 1 (1 + x 2 ) 3 / 2 . 29. f ( x) = x 2 / ( x 3 + 1) R. f ′ ( x) = − x ( x 3 − 1) (1 + x 3 ) 2 . 30. f ( x) = ( a − x ) / ( a + x ) R. f ′ ( x) = − 2 a ( a + x ) 2 . 31. f ( x) = sin x cos x R. f ′ ( x) = cos(2 x ) . 32. f ( x) = e x (sin x + cos x ) R. f ′ ( x) = 2 e x cos x . 33. f ( x) = sin( 1x ) R. f ′ ( x) = − cos(1/x ) x 2 . 34. f ( x) = 1 / sin x R. f ′ ( x) = − cot x csc x . 35. f ( x) = 1 / sin(1/x ) R. f ′ ( x) = cot(1/x)csc(1/x ) x 2 . 36. f ( x) = 1 / ln x R. f ′ ( x) = − 1 x ln 2 ( x ) . 37. f ( x) = x/ ln x R. f ′ ( x) = ln x − 1 ln 2 ( x ) . 1.1. DERIVADAS DIRECTAS 38. f(x) = ln x/x R. f ′ (x)