Learn derivative basics: derivative as the slope of the tangent line
Memorize common derivative rules
Power rule: d/dx(x^n) = n x^(n-1)
Constant rule: d/dx(c) = 0
Constant multiple rule: d/dx(c f(x)) = c f’(x)
Sum/difference rule: d/dx(f(x) ± g(x)) = f’(x) ± g’(x)
Product rule: d/dx(fg) = f’g + fg’
Quotient rule: d/dx(f/g) = (f’g − fg’) / g^2
Chain rule: d/dx(f(g(x))) = f’(g(x)) · g’(x)
Differentiate polynomials using the power rule term-by-term
Use the chain rule for nested functions
Use product/quotient rules when variables are multiplied or divided
Use standard trig derivatives
d/dx(sin x) = cos x
d/dx(cos x) = −sin x
d/dx(tan x) = sec^2 x
d/dx(csc x) = −csc x cot x
d/dx(sec x) = sec x tan x
d/dx(cot x) = −csc^2 x
Use standard exponential derivatives
d/dx(e^x) = e^x
d/dx(a^x) = a^x ln(a)
Use standard logarithm derivatives
d/dx(ln x) = 1/x
d/dx(log_a x) = 1/(x ln a)
Handle radicals with exponents (e.g., √x = x^(1/2))
Simplify the final derivative (combine like terms, reduce fractions)
If needed, verify quickly by plugging in a simple value or checking units/signs
For higher derivatives, differentiate the obtained derivative again using the same rules