One needs to learn derivatives at least in the form they'll be on the test. A lot of high school teachers I had were familiar enough with sorts of questions on

One needs to learn derivatives at least in the form they'll be on the test. A lot of high school teachers I had were familiar enough with sorts of questions on the standardized tests their classes would be taking that they taught these subjects with an artificially narrow focus, in order to boost our grades compared to other schools. Of course, teachers at those schools no doubt did the same. The result is that a lot of people who studied eg. derivatives would be much less able to apply that knowledge in any environment except the standardised test.