Secretaria de Educación Pública
Subsecretaria de Educación Media Superior
Dirección General de Educación Tecnológica Industrial
Centro de Bachillerato Tecnológico Industrial y de Servicios # 124
“Leonardo Bravo”
FORMULARIO BÁSICO DE DERIVADAS
1.
𝑑𝑐
𝑑𝑥 = 0
11.
𝑑 (𝑢𝑛)
𝑑𝑥 = 𝑛 ∙ 𝑢𝑛−1 ∙𝑑𝑢
𝑑𝑥
Elaborado por I.Q. Francisco García Velásquez CBTIS #124 “ Leonardo Bravo”
21.
𝑑 (𝑇𝑎𝑛 𝑢)
𝑑𝑥 = 𝑆𝑒𝑐2𝑢 ∙ 𝑑𝑢
𝑑𝑥
2.
𝑑𝑥
𝑑𝑥 = 1
12.
𝑑 (√𝑢)
𝑑𝑥 =
𝑑𝑢
𝑑𝑥
2√𝑢
22.
𝑑 (𝐶𝑜𝑡 𝑢)
𝑑𝑥 = −𝐶𝑠𝑐2𝑢 ∙ 𝑑𝑢
𝑑𝑥
3.
𝑑 (𝑐 ∙ 𝑢)
𝑑𝑥 = 𝑐 ∙ 𝑑𝑢
𝑑𝑥
13.
𝑑 ( √𝑢
𝑛)
𝑑𝑥 =
𝑑𝑢
𝑑𝑥
𝑛 ∙ √𝑢𝑛−1
𝑛
23.
𝑑 (𝑆𝑒𝑐 𝑢)
𝑑𝑥 = 𝑆𝑒𝑐 𝑢 ∙ 𝑇𝑎𝑛 𝑢 ∙ 𝑑𝑢
𝑑𝑥
4.
𝑑 (𝑢 + 𝑣 − 𝑤)
𝑑𝑥 =𝑑𝑢
𝑑𝑥 +𝑑𝑣
𝑑𝑥 −𝑑𝑤
𝑑𝑥
14.
𝑑 (ln 𝑢)
𝑑𝑥 =
𝑑𝑢
𝑑𝑥
𝑢
24.
𝑑 (𝐶𝑠𝑐 𝑢)
𝑑𝑥 = −𝐶𝑠𝑐 𝑢 ∙ 𝐶𝑜𝑡 𝑢 ∙ 𝑑𝑢
𝑑𝑥
5.
𝑑 (𝑥𝑛)
𝑑𝑥 = 𝑛 ∙ 𝑥𝑛−1
15.
𝑑 (log 𝑢)
𝑑𝑥 =log 𝑒
𝑢∙𝑑𝑢
𝑑𝑥
25.
𝑑 (𝑎𝑟𝑐 𝑆𝑒𝑛 𝑢)
𝑑𝑥 =
𝑑𝑢
𝑑𝑥
√1 − 𝑢2
6.
𝑑 (𝑢 ∙ 𝑣)
𝑑𝑥 = 𝑢 ∙ 𝑑𝑣
𝑑𝑥 +𝑣∙𝑑𝑢
𝑑𝑥
16.
𝑑 (𝑒𝑢)
𝑑𝑥 = 𝑒𝑢∙𝑑𝑢
𝑑𝑥
26.
𝑑 (𝑎𝑟𝑐 𝐶𝑜𝑠 𝑢)
𝑑𝑥 =−𝑑𝑢
𝑑𝑥
√1 − 𝑢2
7.
𝑑 (𝑢 ∙ 𝑣 ∙ 𝑤)
𝑑𝑥 = 𝑢 ∙ 𝑣 ∙ 𝑑𝑤
𝑑𝑥 + 𝑢 ∙ 𝑤 ∙ 𝑑𝑣
𝑑𝑥 + 𝑣 ∙ 𝑤 ∙ 𝑑𝑢
𝑑𝑥
17.
𝑑 (𝑎𝑢)
𝑑𝑥 = 𝑎𝑢∙ln 𝑎 ∙ 𝑑𝑢
𝑑𝑥
27.
𝑑 (𝑎𝑟𝑐 𝑇𝑎𝑛 𝑢)
𝑑𝑥 =
𝑑𝑢
𝑑𝑥
1 + 𝑢2
8.
𝑑 (𝑢
𝑣)
𝑑𝑥 =𝑣 ∙ 𝑑𝑢
𝑑𝑥 −𝑢∙𝑑𝑣
𝑑𝑥
𝑣2
18.
𝑑 (𝑢𝑣)
𝑑𝑥 = 𝑣 ∙ 𝑢𝑣−1 ∙𝑑𝑢
𝑑𝑥 +ln 𝑢 ∙ 𝑢𝑣∙𝑑𝑣
𝑑𝑥
28.
𝑑 (𝑎𝑟𝑐 𝐶𝑜𝑡 𝑢)
𝑑𝑥 =−𝑑𝑢
𝑑𝑥
1 + 𝑢2
9.
𝑑 (𝑐
𝑢)
𝑑𝑥 =−𝑐 ∙ 𝑑𝑢
𝑑𝑥
𝑢2
19.
𝑑 (𝑆𝑒𝑛 𝑢)
𝑑𝑥 = 𝐶𝑜𝑠 𝑢 ∙ 𝑑𝑢
𝑑𝑥
29.
𝑑 (𝑎𝑟𝑐 𝑆𝑒𝑐 𝑢)
𝑑𝑥 =
𝑑𝑢
𝑑𝑥
𝑢√𝑢2− 1
10.
𝑑 (𝑢
𝑐)
𝑑𝑥 =
𝑑𝑢
𝑑𝑥
𝑐
20.
𝑑 (𝐶𝑜𝑠 𝑢)
𝑑𝑥 = −𝑆𝑒𝑛 𝑢 ∙ 𝑑𝑢
𝑑𝑥
30.
𝑑 (𝑎𝑟𝑐 𝐶𝑠𝑐 𝑢)
𝑑𝑥 =−𝑑𝑢
𝑑𝑥
𝑢√𝑢2− 1
