Tabla de derivadas
Matemáticas. Derivación. Cálculo diferencial. Derivada
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| Tabla de Derivadas | |||
| Derivadas y Operaciones con Funciones | |||
| (f + g)(x) (f + g)'(x) = f'(x) + g'(x) | |||
| (f . g)(x) (f . g)(x) = f'(x) . g(x) + f(x) . g'(x) | |||
| (f / g)(x) (f / g)(x) = [ f'(x) . g(x) - f(x) . g'(x)] / g2(x) | |||
| (g o f)(x) (g 0 f)'(x) = g'(fx) . f'(x) | |||
| k f(x) (k.f)'(x) = k . f'(x) | |||
| Derivadas de Funciones | |||
| f(x) = cte. | f'(x) = 0 | f(x) = x | f'(x) = 1 |
| f(x) = x2 | f'(x) = 2x | f(x) = xn | f'(x) = n . xn-1 x>0 |
| f(x) = U(x)n | f'(x) = n . U(x)n-1 . U'(x) | ||
| f(x) = 1 / x | f'(x) = - 1 / x2 | f(x) = 1 / U | f'(x) = - U' / U2 |
| f(x) = ex | f'(x) = ex | f(x) = eU(x) | f'(x) = U' . eU |
| f(x) = ln x Df=R+ | f'(x) = 1 / x | f(x) = ln U(x) | f'(x) = U' / U |
| f(x) = "(x) | f'(x) = 1 / 2"x | f(x) = "[U(x)] | f'(x) = U' / 2"(U) |
| f(x) = sen(x) | f'(x) = cos(x) | f(x) = sen U | f'(x) = U' . cosU |
| f(x) = cos(x) | f'(x) = - sen(x) | f(x) = cos U | f'(x) = - U' . senU |
| f(x) = tg(x) | f'(x) = 1 / cos2(x) | f(x) = tg U | f'(x) = U' / cos2U |
| f(x) = sec(x) | f'(x) = senx / cos2x | f(x) = sec U | f'(x) = (U' . senU) / cos2U |
| f(x) = cosec(x) | f'(x) = - cosx / sen2x | f(x) = cosec U | f'(x) = - (U' . cosU) / sen2U |
| f(x) = cotg(x) | f'(x) = - 1 / sen2(x) | f(x) = cotg U | f'(x) = - U' / sen2U |
| f(x) = arcsen(x) | f'(x) = 1 / "(1 - x2) | f(x)= arcsen U | f'(x) = U' / "(1 - U2) |
| f(x) = arccos(x) | f'(x) = - 1 / "(1 - x2) | f(x) = arcos U | f'(x) = U' / "(1 - U2) |
| f(x) = arctg(x) | f'(x) = 1 / (1 + x2) | f(x) = arctg U | f'(x) = U' / (1 + U2) |