Derivative Table
1. dx
dv
dx
du
)vu(
dx
d±=±
2. dx
du
c)cu(
dx
d=
3. dx
du
v
dx
dv
u)uv(
dx
d+=
4. dx
dv
wu
dx
du
vw
dx
dw
uv)uvw(
dx
d++=
5. 2
vdx
dv
u
dx
du
v
v
u
dx
d−
=
6. (Chain rule) If y = f(u) is differentiable on u = g(x) and u = g(x) is differentiable
on point x, then the composite function y = f(g(x)) is differentiable and
dx
du
du
dy
dx
dy =
7. (Chain rule)
dx
dw
dw
du
du
dy
dx
dy =
8. (Inverse function) If y = f(x) has a non-zero derivative at x and the inverse function
x = f -1(y) is continuous at corresponding point y, then x = f -1(y) is differentiable and:
dx
dy
1
dy
dx =
9. (Parametric equation) For the equation , f(t) and g(t) are differentiable
and f’(t) ≠ 0, then
=
=
)t(gy
)t(fx
dt
dx
dt
dy
dx
dy =.
10. (Parametric equation)
3
3
2
2
2
2
2
2
)'x(
'y''x''y'x
dt
dx dt
dy
dt
xd
dt
yd
dt
dx
dx
yd −
=
−
=
Page 1 of 3
