Problem : Compute the derivative of f (x) = 6x ^{4} +8x ^{3} +12x ^{2} + 24x .
We differentiate term-by-term to get
f'(x) | = | (4)6x ^{3} + (3)8x ^{2} + (2)12x + 24 | |
= | 24(x ^{3} + x ^{2} + x + 1) |
Problem : What is the second derivative of g(x) = sin(x) ?
We have
g'(x) | = | cos(x) | |
g''(x) | = | -sin(x) |
Problem : Let h(x) = - x ^{2} + 3 . For which values of x does h(x) = h'(x) ?
Since h'(x) = - 2x , we want to solve for x in the equation
- x ^{2} + 3 = - 2x |
0 = (x + 1)(x - 3) |