Page 22 - Calc for the Clueless

Rule 3

n
n-1
If f(x) = x , f'(x) = nx . Bring down the exponent and subtract 1 to get the new exponent.
Rule 4

If f(x) = cg(x), f'(x) = cg'(x). If we have a constant c multiplying a function, we leave c alone and only take the
derivative of the function.

Rule 5

If f(x) = g(x) ± h(x), then f'(x) = g'(x) ± h'(x).

In a book, t, u, v, w, x, y, and z are usually variables. a, b, c, and k (since mathematicians can't spell) are used
as constants.

Example 6—

y = 3x + 7x +2x + 3. Find y'.
7
4

Example 7—

Find y' if

a and lib are constants. 9/4 - 1 - 5/4.

-5/11 - 1 = - 16/11. Derivative of messy constants is still 0.

Most calculus books give the derivative of the six trigonometric functions near the beginning. So will we.

Rule 6

A. If y = sin x, y'= cos x.

B. If y = cos x, y' = -sin x.

C. If y = tan x, y' = sec x.
2
2
D. If y = cot x, y' = -csc x.

E. If y = sec x, y' = tan x sec x.