Trap 1: Forgetting the Chain Rule d/dx(sin(3x)) = 3cos(3x), NOT cos(3x). This is the single most common error. Always check if there's an "inner function" that needs differentiating.

Trap 2: Power Rule for Variable Exponents d/dx(x^(sin x)) cannot use the power rule (constant exponent) or exponential rule (constant base). MUST use logarithmic differentiation.

Trap 3: Wrong Parametric Second Derivative d^2y/dx^2 is NOT (d^2y/dt^2)/(d^2x/dt^2). The correct formula is [d/dt(dy/dx)]/(dx/dt).

Trap 4: Domain Errors in Inverse Trig sin^(-1)(sin(2t)) = 2t ONLY when -pi/2 <= 2t <= pi/2. Outside this range, the sign changes. This single trap accounts for more lost marks than any other in differentiation.

Trap 5: Absolute Value in sec^(-1) Derivative d/dx(sec^(-1)(x)) = 1/(|x|sqrt(x^2-1)), not 1/(xsqrt(x^2-1)). The |x| matters for negative x.

Trap 6: Quotient Rule Sign The quotient rule has a MINUS: (f'g - fg')/g^2. Getting the sign wrong flips the answer.

Trap 7: cos^(-1)(cos(x)) is NOT Always x For x in [0, pi]: cos^(-1)(cos x) = x. For x in [pi, 2pi]: cos^(-1)(cos x) = 2pi - x.

Trap 8: Differentiability of |x^n| |x| is NOT differentiable at 0, but |x^3| IS differentiable at 0 (f'(0) = 0). Higher odd powers of x inside absolute value smooth out the corner.