Derivatives

d dx [k] = 0 d dx [x] = 1 d dx [kx] = k d dx [xn] = n · xn – 1  (1) d dx [kxn] = n · kxn – 1  (1) d dx [k · u] = k · u’ d dx [u + v] = u’ + v’  (2) d dx [u – v] = u’ – v’  (3) d dx [uv] = vu’ + uv’  (4) d dx u v  =  vu’ – uv’ v²  (5) d dx [f(u)] = f ’(u) · u’  (6) Power rule    Sum rule Difference Rule    Product rule Quotient rule    Chain rule d dx [ex] = ex d dx [eu] = eu · u’ d dx [ax] = ln(a) · ax d dx [loga(x)] =  1 ln(a) · x d dx [ln(x)] =  1 x d dx [ln(u)] =  'u’ 'u’ d dx [sin(x)] = cos(x) d dx [cos(x)] = –sin(x) d dx [tan(x)] = sec²(x) =  1 cos²(x) d dx [csc(x)] = –csc(x) · cot(x) d dx [sec(x)] = sec(x) · tan(x) d dx [cot(x)] = –csc²(x) d dx [arcsin(x)] =  1 √(1 – x²) d dx [arccos(x)] =  –1 √(1 – x²) d dx [arctan(x)] =  1 1 + x²