Direct Formulas vs Chain Rule: Use direct formulas for simple functions (sin x, $e^x$, $x^n$). Use chain rule whenever the argument is not just x (sin(3x), e^($x^2$), ln(tan x)).

Product Rule vs Logarithmic Differentiation: Product rule is fine for 2-3 factors. For 4+ factors or complicated products/quotients, logarithmic differentiation (take ln, differentiate, multiply by y) is faster and less error-prone.

Implicit vs Explicit: If y can be easily solved in terms of x, do it explicitly. If the equation is symmetric or y cannot be isolated, use implicit differentiation. For equations of form f(x+y) = g(x+y), implicit differentiation often gives dy/dx = -1 directly.

Direct Differentiation vs Simplification: For inverse trig: ALWAYS simplify first. A 30-second substitution saves 5 minutes of error-prone chain rule computation.

Parametric vs Converting to Cartesian: If x(t) and y(t) are given parametrically, use dy/dx = $\frac{dy/dt}{(dx/dt)}$ directly. Don't try to eliminate t unless the resulting Cartesian equation is simpler.

Power Rule vs Logarithmic: Constant exponent: power rule (d/dx($x^5$) = 5$x^4$). Constant base: exponential rule (d/dx(3^x) = 3^x*ln 3). Both variable: logarithmic differentiation.