Calculus 1: Derivatives

Derivative Definition

f'(x) = lim(h→0) [f(x+h) - f(x)] / h; instantaneous rate of change

Power Rule

d/dx [xⁿ] = nxⁿ⁻¹

Constant Rule

d/dx [c] = 0

Sum/Difference Rule

d/dx [f ± g] = f' ± g'

Product Rule

d/dx [fg] = f'g + fg'

Quotient Rule

d/dx [f/g] = (f'g - fg') / g²

Chain Rule

d/dx [f(g(x))] = f'(g(x)) · g'(x)

d/dx [sin x]

cos x

d/dx [cos x]

-sin x

d/dx [tan x]

sec²x