Pattern 1: Inverse Trig Simplification (Most Frequent) Questions give y = sin^(-1)(expression) or tan^(-1)(expression) where the expression is a double/triple angle formula in disguise. Always substitute x = sin t, cos t, or tan t.

Pattern 2: Logarithmic Differentiation y = $x^x$, y = (sin x)^(cos x), or y = product of many terms. Take ln, differentiate, multiply by y.

Pattern 3: Self-Referential Functions f(x) = $x^3$ + $x^2$f'(1) + xf''(2) + f'''(3). Set up equations for f'(1), f''(2), f'''(3) and solve.

Pattern 4: Parametric Curves Cycloid, astroid, involute. Find dy/dx and $d^{2y}$/$dx^2$.

Pattern 5: Infinite Nested Radicals y = sqrt(f(x) + sqrt(f(x) + ...)). Write $y^2$ = f(x) + y, differentiate implicitly.

Pattern 6: Differentiability Counting Count non-differentiable points of |f(x)|, max(f,g), or piecewise functions.

Scoring Strategy:

• Master inverse trig simplification (1-2 questions guaranteed)
• Practice logarithmic differentiation patterns
• Know parametric second derivative formula
• Check differentiability at junction points