0.3333
-3 over x4
The inverse of a number is 1 divided by that number. So the inverse of x3 + 1 is 1/(x3 + 1).
x4/12 since derivative of x4/12 is 4x3/12 or x3/3
lim (x3 + x2 + 3x + 3) / (x4 + x3 + 2x + 2)x > -1From the cave of the ancient stone tablets, we cleared away several feet of cobwebs and unearthed"l'Hospital's" rule: If substitution of the limit results in ( 0/0 ), then the limit is equal to the(limit of the derivative of the numerator) divided by (limit of the derivative of the denominator).(3x2 + 2x + 3) / (4x3 + 3x2 + 2) evaluated at (x = -1) is:(3 - 2 + 3) / (-4 + 3 + 2) = 4 / 1 = 1
the derivative of 3x is 3 the derivative of x cubed is 3 times x squared
-12sin(x3)x2
(x3)'=3x2(x3)''=(3x2)'=6x
The first derivative of ln x is 1/x, which (for the following) you better write as x-1.Now use the power rule:Second derivative (the derivative of the first derivative) is -1x-2, the third derivative is the derivative of this, or 2x-3. You may now wish to write this in the alternative form, as 2 / x3.
Write it as (1/3)x and take the derivative. You get (1/3)x0 = 1/3 * 1 = 1/3 ■
Let y = x3 - 8, then y' = 3x2 + 0 = 3x2.
-4 / x3
1.6667
10/x3 = 10 x-3d/dx(10x-3) = -30 x-4 = -30/x4