Formulario di Analisi Matematica I

Derivate fondamentali

D [k] = 0

D [x] = 1

D [xⁿ] = n x^n-1

D [a^x] = a^x ln(a)

D [e^x] = e^x

D [log_a(x)] = 1 / (x ln(a))

D [sen x] = cos x

D [cos x] = -sen x

D [tg x] = 1 / cos² x

D [cotg x] = -1 / sen² x

D [arcsen x] = 1 / √(1 - x²)

D [arccos x] = -1 / √(1 - x²)

D [arctg x] = 1 / (1 + x²)

D [arccotg x] = -1 / (1 + x²)

Grafici di funzioni elementari

• y = ax + b
• y = |x|
• y = xⁿ (n pari)
• y = xⁿ (n dispari)
• y = a^x
• y = log_a(x)
• y = sen x
• y = cos x
• y = tg x
• y = cotg x
• y = arcsen x
• y = arccos x
• y = arctg x
• y = arccotg x

Integrali fondamentali

∫ xⁿ dx = xⁿ⁺¹ / (n + 1) + c (n ≠ -1)

∫ a^x dx = a^x / ln(a) + c

∫ e^x dx = e^x + c

∫ sen x dx = -cos x + c

∫ cos x dx = sen x + c

∫ 1 / cos² x dx = tg x + c

∫ 1 / sen² x dx = -cotg x + c

∫ 1 / x dx = ln |x| + c

∫ 1 / (1 + x²) dx = arctg x + c

∫ 1 / √(1 - x²) dx = arcsen x + c

∫ -1 / √(1 - x²) dx = arccos x + c