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IBP reverses the product rule. The LIATE mnemonic tells you which function to differentiate.

One gives a function, the other a number. Understanding the difference is essential for every integration technique.

Every standard integration rule with derivations, visual patterns, and worked examples.

Integration is the inverse of differentiation and the tool for computing areas, volumes, and accumulation.

Where derivatives live in the real world: velocity, growth rates, tangent lines, maximum and minimum values.

Optimization is calculus applied to decisions: maximize profit, minimize cost, find the ideal dimensions.

The second derivative measures concavity. The third measures jerk. Here's when and why to go higher.

sin, cos, tan and all six trig functions — their derivatives, proofs and most common applications.

Implicit differentiation lets you find dy/dx for curves that can't be written as y = f(x). Here's how.

The Chain Rule is the most powerful differentiation tool. Once you see the pattern it becomes automatic.