Derivatives - ALL

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d/dx (x)
=1
d/dx (x^n)
=n x^(n-1)
d/dx (a)
=0
d/dx [f(x)g(x)]
=f(x)g'(x) + g(x)f'(x)
d/dx [f(x)/g(x)]
=g(x)f'(x)-f(x)g'(x)/g(x)^2
d/dx [f(g(x))]
=f'(g(x))g'(x)
d/dx sin(x)
=cosx
d/dx sin(u)
=(cosu)u'
d/dx cos(x)
=-sinx
d/dx cos(u)
= -(sinu) u'
d/dx tanx
= sec^2(x)
d/dx tan(u)
= (sec^2u) u'
d/dx cot(x)
= -csc^2(x)
d/dx cot(u)
= -(csc^2u) u'
d/dx sec(x)
= secxtanx
d/dx sec(u)
= (secutanu) u'
d/dx csc(x)
= -cscxcotx
d/dx csc(u)
=-(cscucotu) u'
d/dx arcsin(x)
=1/√(1-x²)
d/dx arcsin(u)
=u'/√(1-u²)
d/dx arccos(x)
=-1/√(1-x²)
d/dx arccos(u)
=-u'/√(1-u^2)
d/dx arctan(x)
=1/(1+x²)
d/dx arctan(u)
=u'/(1+u²)
d/dx arccot(x)
=-1/(1+x²)
d/dx arccot(u)
=-u'/(1+u²)
d/dx arcsec(x)
=1/x√(x²-1)
d/dx arcsec(u)
=u'/u√(u²-1)
d/dx arccsc(x)
=-1/x√(x²-1)
d/dx arccsc(u)
=-u'/u√(u²-1)
d/dx eˣ
= eˣ
d/dx e^u
= e^u * u'
d/dx aˣ
= aˣ ln(a)
d/dx a^u
= (ln a)·a^u·u'
d/dx ln(x)
= 1/x
d/dx ln(u)
= u'/u
d/dx log(a)x
= 1/[(lna)(x)]
d/dx log(a)u
= [u']/[(lna)(u)]