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Derivative of a constant is
zero:
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d
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c = 0
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dt
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Derivative of t with respect
to itself is 1:
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d
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t = 1
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dt
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A constant can be factored
out:
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d(cx)
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= c
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dx
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dt
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dt
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Derivative of a sum is the
sum of derivatives:
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d(x+y)
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=
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dx
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+
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dy
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dt
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dt
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dt
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Derivative of a 2nd order
polynomial:
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dt2
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= 2
t
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dt
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Derivative of an n-th order
polynomial:
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dtn
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= n
tn-1
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dt
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Product rule:
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d(x·y)
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=
y
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dx
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+ x
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dy
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dt
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dt
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dt
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Derivative of sine is a
cosine:
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d
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sin(t) =
cos(t)
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|
|
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dt
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Derivative of a cosine is a
negative sine:
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d
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cos(t) = -
sin(t)
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|
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dt
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The exponential function is
its own derivative:
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d
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exp(t) =
exp(t)
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|
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dt
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Derivative of a natural
logarithm:
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d
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ln(t) =
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1
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dt
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t
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Chain rule; z is a function
of x here:
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d
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z(x(t)) =
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dz
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·
|
dx
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dt
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dx
|
dt
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|