Basic Differentiation Formulas
In the table below, and represent differentiable functions of ? œ 0 ÐBÑ @ œ 1ÐBÑ B
Derivative of a constant
.-
.B œ!
Derivative of constant ( ) We could also write , and could use ..?
.B .B
ww
-? œ - Ð Ð-0Ñ œ -0
the “prime notion” in the other formulas as well)multiple
Derivative of sum or ()
..?.@
.B .B .B
?„@ œ „
difference
Product Rule (
..@.?
.B .B .B
?@ќ? @
Quotient Rule ()
.?
.B @ œ@?
@
.? .@
.B .B
#
Chain Rule .C .C
.B .? .B
.?
œ
...?
.B .B .B
88" 88"
Bœ8B ?œ8?
(ln ) (ln )
...?
.B .B .B
BB ??
+œ ++ +œ ++
(If = ) +/ /œ/ /œ/
...?
.B .B .B
BB ??
log log
...?
.B + B .B + ? .B
++
Bœ ?œ
11
(ln ) (ln )
(If ) ln ln +œ/ B œ ? œ
...?
.B B .B ? .B
11
sin cos sincos
...?
.B .B .B
Bœ B ?œ ?
cos sin cos sin
...?
.B .B .B
Bœ B ?œ ?
tan sec tansec
...?
.B .B .B
##
Bœ B ?œ ?
cot csc cot csc
...?
.B .B .B
##
Bœ B ?œ ?
sec sec tan sec sec tan
...?
.B .B .B
Bœ B B ?œ ? ?
csc csc cot csc csc cot
...?
.B .B .B
Bœ B B ?œ ? ?
sin sin
..
.B .B
" "
Bœ ?œ
arcsin arcsin
...?
.B .B .B
"B "?
Bœ ?œ
11
ÈÈ
##
tan tan ..
.B .B
" "
Bœ ?œ
arctan = arctan =
...?
.B "B .B "? .B
B?
11
##