3'7 Higher Order Derivatives

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3.7 Higher Order Derivatives
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Notations
Second Derivative
Third Derivative
Forth Derivative
nth Derivative
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You Try It
Determine the first and second derivative of the
following. Use the TI-89 to check your
results. 1. g(x) (2x 1) / (x 1) 2.
f(t) t3sin(t) 3. h(x) tan-1(x2)
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With Implicit Differentiation
Use implicit differentiation to find the second
derivative of
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General Derivatives
Example Determine f (n)(x) if f(x)x1/2.
Example Determine D1000 xe-x.
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Rectilinear Motion
If s(t) represents the position function for a
particle, then what does the following represent?
v(t) the velocity function.
a(t) the acceleration function.
j(t) the jerk function.
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Rectilinear Motion
Example Let s(t) 2t3 7t2 4t 1 be the
position of a particle (in meters) at time t (in
seconds). Determine (a) the velocity and
acceleration functions, (b) the acceleration
after one second, and (c) the acceleration at the
instant the velocity is zero.
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Differential Equation
An equation whose solution is an unknown function.
Example Find constants A, B, and C such that the
function y Ax2 Bx C satisfies the
differential equation y'' y' 2y x2.