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Math 124 – Week 6
Student Guide:
Week 6 is devoted to developing further basic derivative topics:
the chain rule, implicit derivatives and higher order derivatives.
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The chain rule is one of the most powerful rules for calculating
derivatives and this needs to be mastered thoroughly.
- We are able to calculate tangent lines to graphs of functions y=f(x) using the derivative f'(x).
However, what if the curve we are interested in is not the graph of a function?
It still makes sense to discuss tangent lines to curves which are not the graphs of
functions, like a circle, or ellipse, etc. How do we proceed?
The technique required is called "implicit differentiation".
- The homework
contains further challenging applications of the derivative.
One of the homework problems will introduce an important fact about parametric motion:
tangent lines to parametrized curves can be computed using horizontal and vertical velocities.
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