Find the derivative of the following functions: (Please show steps)

Question

1. f(x)= secx = 1/cosx
2. 2. f¹(x) = 1/2x
3. If f¹(x)=4(x), then f(x) is

Answer 1

In the first two use the quotient rule. A mnemonic my students taught me is: downsie d upside - upsie d downsie divided by downsie squared.

The third one is f"(x)=4.

The first one is a standard derivative (sec x tan x) but you get it this way (use thee mnemonic)

(0 + sin x)/cos²x = sec x tan x.

The second one is (0-2)/x² = -2/x²