Formulas Derivative - West Virginia University
math.wvu.edu › Formulas-Derivative1. Basic Derivative formulae (xn)0 = nxn−1 (ax)0 = ax lna (ex)0 = ex (log a x) 0 = 1 xlna (lnx)0 = 1 x (sinx)0 = cosx (cosx)0 = −sinx (tanx)0 = sec2 x (cotx)0 = −csc2 x (secx)0 = secxtanx (cscx)0 = −cscxcotx (sin−1 x)0 = 1 √ 1−x2 (cos−1 x)0 = −1 √ 1−x2 (tan−1 x)0 = 1 1+x2 (cot−1 x)0 = −1 1+x2 (sec−1 x)0 = 1 x √ x2 −1 (csc−1 x)0 = −1 x √ x2 −1 2. Di๏ฌerentiation Rules
Derivative Rules and Formulas - UH
www.math.uh.edu › ~bekki › 1432Derivative Rules and Formulas Rules: (1) f 0(x) = lim h!0 f(x+h) f(x) h (2) d dx (c) = 0; c any constant (3) d dx (x) = 1 (4) d dx (xp) = pxp 1; p 6= 1 (5) d dx [f(x) g(x)] = f0(x) g0(x) (6) d dx (cf(x)) = cf0(x) (7) d dx [ f x)g)] = )+ (8) d dx f(x) g(x) = f0(x)g(x) f(x)g0(x) (g(x))2 (9) d dx 1 g(x) = g0(x) (g(x))2 (10) d dx [ f (g x))] = 0)) 0) (11) d dx f 1(x) = f 1 0 (x) = 1 f0(f 1(x))