Derivative Forms Memorize the following derivative forms. 1. d dx
Transcription
Derivative Forms Memorize the following derivative forms. 1. d dx
math 251 (Bradford) Derivative Forms Memorize the following derivative forms. d dx 1. 2. d dx 3. d dx 4. d dx 5. d dx sin u = cos(u) cos u tan u du dx du = − sin(u) dx = sec2 (u) du dx sec u = sec(u) tan(u) du dx 7. d dx d dx 8. d dx 9. u n u = n un−1 = eu e cot u du dx du dx = − csc2 (u) du dx = − csc(u) cot(u) csc u du dx k = 0 d f (g(x)) = f 0 (g(x)) g 0 (x) dx Chain Rule Product Rule Sum/Difference Formula d dx 6. d dx f (x) ± g(x) 0 d dx 0 = f (x) ± g (x) f (x) · g(x) Constant Multiple Rule Quotient Rule d dx d dx k f (x) 0 = k f (x) 1 u(x) v(x) = = f (x) · g 0 (x) + f 0 (x) · g(x) v(x) · u0 (x) − u(x) · v0 (x) [v(x)]2