Properties of Derivatives
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(d/dt)cos(wt)
-wsin(wt)
(dC)/(dt) [C is constant]
0
(d/dt)ln(bt)
1/t
(d/dt)e^(bt)
b(e^(bt))
(d(t^n))/(dt)
nt^(n-1)
The derivative of a constant times a function equals...
the constant times the function
The derivative of a product of functions f(t)g(t) equals...
the first function times the derivative of the second plus the second function times the derivative of the first
Given f(x) and x(t), the derivative of f(t) equals...
the product of the derivative of f with respect to x and the derivative of x with respect to t
The derivative of t with respect to x is...
the reciprocal of the derivative of x with respect to t
The derivative of a sum of functions equals...
the sum of the derivatives of the functions
(d/dt)tan(wt)
w(sec^2)(wt)
(d/dt)sin(wt)
wcos(wt)