Trick 1: Recognize inverse trig patterns instantly If you see 2x/(1+x^2), (1-x^2)/(1+x^2), or 2x/(1-x^2) inside inverse trig, substitute x = tan(t).

Trick 2: Use symmetry d/dx[sin^(-1)(x) + cos^(-1)(x)] = 0 because sin^(-1)(x) + cos^(-1)(x) = pi/2 (constant). Similarly, tan^(-1)(x) + cot^(-1)(x) = pi/2.

Trick 3: Reciprocal derivatives If y = f(x) and x = f^(-1)(y), then dx/dy = 1/(dy/dx). Useful when differentiating inverse functions.

Trick 4: For dy/dx of y = f(x) at a specific point Sometimes plugging in the point AFTER finding the general derivative is harder than using implicit differentiation directly at the point.

Trick 5: Factor before differentiating Before differentiating a quotient, check if the numerator can be factored to cancel with the denominator. This avoids messy quotient rule applications.

Trick 6: Recognize derivative of ln|f(x)| d/dx[ln|f(x)|] = f'(x)/f(x). This appears frequently in integration but is useful in differentiation too.