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Calculus help — limits, derivatives, integrals, every step shown
Calculus is where math 'opens up' — and where most students hit a wall. The good news: 90% of calculus questions reduce to a small set of patterns. Once you recognise the pattern (chain, product, parts, substitution), the rest is mechanical.
Find d/dx of (3x² + 2x)·sin(x) using the product rule, then evaluate at x = π/2.
Try it with your own question →Why calculus is harder than it looks
Calculus stacks abstraction on abstraction. Limits feel philosophical until you've done 50 of them. Derivatives are mechanical once the rules click. Integration requires creativity. Most students hit different walls at different stages — and that's normal.
The differentiation decision tree
Every derivative question is one of: power rule, product rule, quotient rule, chain rule, implicit, or trig/log/exp. The trick is identifying which in 3 seconds. We teach the tree: 'Does it have a function inside another function? Chain rule. Two functions multiplied? Product rule. Two functions divided? Quotient rule. Otherwise, power rule + table look-ups.'
Integration is harder — and there's a reason
Differentiation has rules that always work. Integration requires you to recognise patterns and reverse-engineer them. That's why integration tables exist. We don't just give you the antiderivative — we walk through which substitution, parts choice (LIATE rule), or trig identity unlocks it.
Word problems people actually fail on
Optimisation (max/min), related rates, and area between curves are the three calculus word-problem types that show up in nearly every exam. Each has a setup pattern. We've seen students go from 'I can't do these' to 'these are my easiest marks' in two weeks once they internalise the setup.
Series and convergence (BC / A2 / HL)
For Calc BC, A2 Pure, or IB HL: the series tests (ratio, root, integral, comparison, alternating) are infamous for tripping up students. We can walk through which test to apply and why — and the algorithmic checklist that prevents you from picking the wrong one.
What we do specifically well for calculus
- Differentiation in step-by-step with rule named
- Integration with substitution / parts choice justified
- Visual graph plotting alongside the algebra
- Definite-integral solver showing each working step
- Word problem setups (related rates, optimisation, area)
- Series convergence test walkthroughs
Topics covered
Tools that pair well with calculus
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