A big part of making math problems easier is recognizing simplification patterns.
Hence, Cool 12 Second Math Tricks! More detailed steps follow each video
1. The first expression is the derivative of a logarithm. It's just a matter of seeing it.
2. Remember the chain rule vernocular: "The derivative of the whole thing is equal to the derivative of the outside times the derivative of the inside". You can read every little detail here at Wikipedia.