Higher-Order Derivatives
Higher-order derivatives are attained by iteratively taking the derivatives of resulting derivatives. Thus, the second derivative of a function is the derivative of its first derivative and the nth-order derivative may be attained by taking the derivative of the (n − 1)st-order derivative.
Various notations may be used to denote successive derivatives:
Example #1:
Find the first five derivatives of sin x.
Solution #1:
Example #2:
Find the first three derivatives of 4x3 + 2x + 6.
Solution #2:
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