Summary of Differentiation Rules

Constant Rule (General Differentiation Rules)

d/dx[c] = 0, [c] is a real number

Constant Multiple Rule (General Differentiation Rules)

d/dx[cu] = cu’, c is a real number

Product Rule (General Differentiation Rules)

d/dx[uv] = uv’ + vu’

Chain Rule #1 (General Differentiation Rules)

• d/dx[f (u) ] = f ’(u) u ’

Chain Rule #2 (Derivatives of Trig functions)

d/dx[sin x] = cos x

Chain Rule #3 (Derivatives of Trig functions)

d/dx[sec x] = sec x tan

Chain Rule #4 (Derivatives of Trig functions)

d/dx[cot x] = -csc²x

Chain Rule #5 (Derivatives of Exponential and Logarithmic)

d/dx[e^x] = e^x

Chain Rule #6 (Derivatives of Exponential and Logarithmic)

d/dx[a^x] = (ln a)a^x

Chain Rule #7 (Derivatives of Exponential and Logarithmic)

a is a positive real number (a ≠ 1)

(Simple) Power Rule (General Differentiation Rules)

d/dx[xⁿ] = nx^n-1, d/dx[x] = 1 n is a rational number

Sum or Difference Rule (General Differentiation Rules)

d/dx[u +- v] = u’ +- v’

Quotient Rule (General Differentiation Rules)

d/dx [u/v] = vu’ - uv’/v²

General Power Rule #1 (General Differentiation Rules)

d/dx[uⁿ] = nu^n-1, n is a rational number

General Power Rule #2 (Derivatives of Trig functions)

d/dx[tan x[ = sec²x

General Power Rule #3 (Derivatives of Trig functions)

d/dx[cos x] = -sin x

General Power Rule #4 (Derivatives of Trig functions)

d/dx[csc x] = -csc x cot x

General Power Rule #5 (Derivatives of Exponential and Logarithmic)

d/dx[ln x] = 1/x’ x>0

General Power Rule #6 (Derivatives of Exponential and Logarithmic)

d/dx[log_ax] = 1/(1na)x’