Derivative of Common Functions

derivative of sinx

cosx

derivative of cosx

-sinx

derivative of e^x

e^x

derivative of lnx

1/x

derivative of log_bx

1/(lnb)x

derivative of tanx

sec²x

derivative of cotx

-csc²x

derivative of secx

secxtanx

derivative of cscx

-cscxcotx

derivative of sinu

(cosu)u’

derivative of tanu

(sec²u)u’

derivative of secu

(secu*tanu)u’

derivative of cosu

-(sinu)u’

derivative of cosu

-(sinu)u’

derivative of tanu

(sec²u)u’

derivative of cotu

-(csc²u)u’

derivative of secu

(secutanu)u’

derivative of cscu

-(cscucotu)u’

derivative of lnu

1/u * u’

derivative of e^u

e^u * u’

derivative of a^x

(lna)a^x

derivative of a^u

(lna)a^uu’

derivative of log_ax

1/(lna)x

derivative of log_au

1/(lna)u * u’

derivative of arcsinx or sin^-1x

1/sqrt(1-x²)

derivative of arccosx or cos^-1x

-1/sqrt(1-x²)

derivative of arctanx or tan^-1x

1/(1+x²)

derivative of arccotx or cot^-1x

-1/(1+x²)

derivative of arcsecx or sec^-1x

1/(lxl*sqrt(x²-1))

derivative of arccscx or csc^-1x

-1/(lxl*sqrt(x²-1))

derivative of arcsinu or sin^-1u

u’/sqrt(1-u²)

derivative of arccosu or cos^-1u

-u’/sqrt(1-u²)

derivative of arctanu or tan^-1u

u’/(1+u²)

derivative of arccotu or cot^-1u

-u’/(1+u²)

derivative of arcsecu or sec^-1u

u’/(lul*sqrt(u²-1))

derivative of arccscu or csc^-1u

-u’/(lul*sqrt(u²-1))

derivative of an inverse function

[f^-1(y)]' = 1/(f’(x) if f(x) = y