Derivatives of More Complicated Functions

Since most functions are complicated, we need some more rules. Next: how to find derivatives of functions that
were built by taking sums, products, and quotients of simpler functions.

The "prime" notation will become more useful as the functions become more complicated. If we have some expression

□

then we can write the derivative of that expression as

(□)'.

Sample Problem

(x²)' denotes the derivative of x².

Sample Problem

If f(x) = 5x + 6, then f'(x) and (5x + 6)' mean the same thing.

Sample Problem

(4sin(x) + e^x)' denotes the derivative of 4sin(x) + e^x (we'll know how to find this soon).

Be Careful: Whenever possible, simplify the function before finding its derivative.