TABLE OF CONTENTS
Find the third derivative of the function f(x) = 5x4 + 4x3 - 7x2.
We'll find each derivative along the way. The first derivative is
f (1)(x) = 20x3 + 12x2 - 7x.
We take another derivative to find the second derivative of f :
f (2)(x) = 60x2 + 24x - 7.
Finally, one more time to find the third derivative of f:
f (3)(x) = 120x + 24.
Find the fifth derivative of the function f(x) = 5x4 + 4x3 - 7x2.
We already know the third derivative:
We differentiate again:
f (4)(x) = 120
One more time. Since the derivative of a constant is zero,
f (5)(x) = 0.
Let f (x) = sin x. Find f (101) (x).
We need to know whether 101 differs by a multiple of 4 from 1, 2, 3, or 4. Since 101 is different from 1 by 100, which is a multiple of 4,
f (101)(x) = f (1)(x) = cos x.