Use the power rule: d/dx(x^n) = n x^(n-1)
Use the constant rule: d/dx(c) = 0
Use the constant multiple rule: d/dx[c f(x)] = c f'(x)
Use the sum rule: d/dx[f(x) + g(x)] = f'(x) + g'(x)
Use the difference rule: d/dx[f(x) – g(x)] = f'(x) – g'(x)
Use the product rule: d/dx[f(x)g(x)] = f'(x)g(x) + f(x)g'(x)
Use the quotient rule: d/dx[f(x)/g(x)] = [f'(x)g(x) – f(x)g'(x)] / [g(x)]^2
Use the chain rule: d/dx[f(g(x))] = f'(g(x))g'(x)
Differentiate exponentials: d/dx(e^x) = e^x, d/dx(a^x) = a^x ln(a)
Differentiate logarithms: d/dx(ln x) = 1/x, d/dx(log_a x) = 1/(x ln a)
Differentiate trig functions: d/dx(sin x) = cos x, d/dx(cos x) = -sin x, d/dx(tan x) = sec^2 x
Differentiate inverse trig functions: d/dx(arcsin x) = 1/sqrt(1-x^2), d/dx(arccos x) = -1/sqrt(1-x^2), d/dx(arctan x) = 1/(1+x^2)
Apply implicit differentiation when x and y are mixed
Apply logarithmic differentiation for products, quotients, and powers
Simplify the expression after differentiating
Check for domain restrictions and points where the derivative may not exist