This document contains a table summarizing the derivatives of common functions. It lists functions and their derivatives, grouped by type of function. The types of functions included are sums and differences, products, quotients, composite functions, powers, exponentials, logarithmic functions, trigonometric functions, and inverse trigonometric functions. For each function, it gives the derivative of that function with respect to x.

1. TABLA DE DERIVADAS
SUMA Y RESTA y = f(x) + g(x) y´= f´(x) + g´(x)
PRODUCTO POR UN
NÚMERO
y = k · f(x) y´= k · f´(x)
PRODUCTO y = f(x) · g(x) y´= f´(x) · g(x) + f(x) · g´(x)
COCIENTE y =
)x(g
)x(f
y´=
( )2
)x(g
)x´(g)x(f)x(g)x´(f ⋅−⋅
REGLA DE LA
CADENA
y = f[g(x)] y´= f´[g(x)] · g´(x)
POTENCIAS
y = xn
y´= n · xn–1
y = [f(x)]n
y´= n · [f(x)]n–1
· f´(x)
y = k y´= 0
y = x y´= 1
y = x y´=
x2
1
y = )x(f y´= )x´(f
)x(f2
1
⋅
EXPONENCIALES
y = ex
y´= ex
y = ef(x)
y = ef(x)
· f´(x)
y = ax
y´= ax
· ln a y = af(x)
y´= af(x)
· ln a · f´(x)
LOGARÍTMICAS
y = ln x y´=
x
1
y = ln f(x) y´= )x´(f
)x(f
1
⋅
y = loga x y´=
aln
1
x
1
⋅ y = loga f(x) y´= )x´(f
aln
1
x
1
⋅⋅
TRIGONOMÉTRICAS
y = sen x y´= cos x y = sen f(x) y´= cos f(x) · f´(x)
y = cos x y´= –sen x y = cos f(x) y´= –sen f(x) · f´(x)
y = tg x
y´= 1 + tg2
x
y´= sec2
x
y´= 2
1
cos x
y = tg f(x)
y´= [1 + tg2
f(x)] · f´(x)
y´= sec2
f(x) · f´(x)
y´= 2
1
f´(x)
cos f(x)
⋅
y = cotg x
y´= –1 – cotg2
x
y´= –cosec2
x
y´= 2
1
sen x
− y = tg f(x)
y´= [–1 – cotg2
f(x)] · f´(x)
y´= –cosec2
f(x) · f´(x)
y´= 2
1
f´(x)
sen f(x)
−
⋅
y = arcsen x y´= 2
1
1 x−
y = arcsen f(x) y´= 2
1
f´(x)
1 (f(x))
⋅
−
y = arccos x y´= 2
1
1 x
−
−
y = arccos f(x) y´= 2
1
f´(x)
1 (f(x))
−
⋅
−
y = arctg x y´= 2
1
1 x+
y = arctg f(x) y´= 2
1
f´(x)
1 (f(x))
⋅
+