Derivative Rules: If u is a function of x, then: 1) d(un ) dx dx 2) d(ln u

Derivative Rules: If u is a function of x, then: 1) d(un ) dx dx 2) d(ln u

Derivative Rules: If u is a function of x, then:
1)
d(u n )
du
= nu n −1
dx
dx
2)
d(ln u) 1 du
=
dx
u dx
3)
d(sinu)
du
= cosu
dx
dx
4)
d(cosu)
du
= − sinu
dx
dx
5)
d(tanu)
du
= sec 2 u
dx
dx
6)
d(cotu)
du
= − csc 2 u
dx
dx
7)
d(secu)
du
= secutanu
dx
dx
8)
d(cscu)
du
= − cscucotu
dx
dx
9)
d(e u )
du
= eu
dx
dx
10)
d(a u )
du
= a u lna
dx
dx
11)
d(sin −1 u)
1
du
=
dx
1− u 2 dx
12)
d(tan − 1 u)
1 du
=
dx
1 + u 2 dx
13)
d(sec −1 u)
1
du
=
2
dx
u u −1 dx
Product Rule: Dx [fg] = fg′ + f ′g
Quotient Rule: Dx
f gf ′ − fg′
=
g
g2