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You learn calculus fast by making sure you understand each aspect before proceeding to the next. Do not be overwhelmed when you see the big picture - just decompose it into its parts, and remember what each transformation actually means.

This means you need to understand how limits factor into the slope of a curve, and you need to understand how the reverse transformation figures into the area under a curve.

Calculus is actually easy. What usually trips us up is the underlying mathematics, geometry, trigonometry, etc. that forms the basis for everything we do with calculus. If you do not have a solid grasp of the underlying prerequisites, you will not understand the transformations that calculus performs.

Yes, there is a lot of memorization but, get the basics, and know how to combine them, and you have got it made.

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Q: How do you learn calculus fast?
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