To find the rate of change.
Velocity, for example, is the rate of change of distance - in a specified direction. Acceleration is the rate of change of velocity.
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The idea is to use the addition/subtraction property. In other words, take the derivative of 5x, take the derivative of 1, and subtract the results.
There are many uses in mathematics for derivative rules in order to derive from formulas. The main use of using derivative rules for mathematical formulas is to differentiate the logarithm.
"Derivative of"
Write sec x as a function of sines and cosines (in this case, sec x = 1 / cos x). Then use the division formula to take the first derivative. Take the derivative of the first derivative to get the second derivative. Reminder: the derivative of sin x is cos x; the derivative of cos x is - sin x.
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