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u-substitution reverses the chain rule. Recognise the pattern and 90% of integrals become straightforward.

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.

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

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

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

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

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

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