University:
Whitman College
Course:
MATH-126 | Calculus II
Academic year:

2024
Views:

376

Pages:

1
Author:

Nadia Cooke

Table of Derivatives Below is a table of derivatives we should be familiar with. 0 f f cf cf 0 0 f ±g f ± g0 fg f 0g + f g0 f (g(x)) f 0 (g(x))g 0 (x) f g f 0 g−f g 0 g2 f (x)g(x) Use log diff. f f0 c 0 n x nxn−1 x e ex ax ax ln(a) 1 ln |x| x f f0 sin(x) cos(x) cos(x) − sin(x) sec2 (x) tan(x) sec(x) sec(x) tan(x) csc(x) − csc(x) cot(x) cot(x) − csc2 (x) √ 1 sin−1 (x) 1−x2 1 tan−1 (x) 1+x2 Table of Antiderivatives Below is a table of antiderivatives that we get by taking the derivative table and swapping columns. The arbitrary constant has been left off to save space. f F cf cF f ±g F ±G f c xn 1/x ex F cx 1 xn+1 n+1 ln |x| ex In Class Example 1 f F cos(x) sin(x) sin(x) − cos(x) sec2 (x) tan(x) sec(x) tan(x) sec(x) √ 1 sin−1 (x) 1−x2 1 tan−1 (x) 1+x2

Table of Derivatives - Cheat Sheet

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