9. Higher Derivatives
by M. Bourne
We can continue to find the derivatives of a derivative. We find the
- second derivative by taking the derivative of the first derivative,
- third derivative by taking the derivative of the second derivative... etc
If `y=x^5+3x^3-2x+7`, then what are the higher derivatives?
Application - Acceleration
We saw before that acceleration is the rate of change of velocity:
But we also know that velocity is the rate of change of displacement:
So it follows that the second derivative of displacement will give us acceleration:
If the displacement (in metres) at time t (in seconds) of an object is given by
s = 4t3 + 7t2 − 2t,
find the acceleration at time `t = 10`.
Higher Derivatives of Implicit Functions
a. Find the second derivative of the implicit function xy + y2 = 4.
b. Find the value of the second derivative of the implicit function in part (a) when x = 2, where y > 0.