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Basic Differentiation Formulas http://www.math.wustl.edu/~freiwald/Math131/derivativetable.pdf In the table below, ? œ 0 ÐBÑ and @ œ 1ÐBÑ represent differentiable functions of B Derivative of a constant Derivative of constant multiple Derivative of sum or difference Product Rule Quotient Rule
..B . .B . .B

œ ! (-?) œ -

.? .B .? .B

ÐWe could also write Ð-0 Ñ w œ -0 w , and could use the “prime notion” in the other formulas as well) „
.@ .B

(? „ @) œ

. .B . .B

.@ (?@Ñ œ ? .B  @

.? .B

(?) œ @
.C .? .? .B

.@ @ .? ? .B .B # @

Chain Rule

.C .B

œ

. .B

B8 œ 8B8"

. .B

?8 œ 8?8"

.? .B

. .B

+B œ (ln +) +B /B œ /B log+ B œ ln B œ
1 B 1 (ln +) B

. .B . .B . .B . .B

+? œ (ln +) +? /? œ /?
.? .B

.? .B

(If + = / )

. .B . .B

log+ ? œ ln ? œ

1 .? (ln +) ? .B

(If + œ / )

. .B

1 .? ? .B

. .B . .B . .B . .B . .B . .B . .B

sin B œ cos B cos B œ  sin B tan B œ sec# B cot B œ  csc# B sec B œ sec B tan B csc B œ  csc B cot B sin" B œ
. .B

. .B . .B . .B . .B . .B . .B . .B 1 È"B#

sin ? œ cos ?

.? .B .? .B

cos ? œ  sin ? tan ? œ sec# ?
.? .B

cot ? œ  csc# ?

.? .B .? .B .? .B

sec ? œ sec ? tan ?

csc ? œ  csc ? cot ? sin" ? œ
. .B

arcsin B œ

arcsin ? œ

1 È"?#

.? .B

. .B

tan" B œ
. .B

. .B 1 "B#

tan" ? œ
. .B

arctan B =

arctan ? =

1 .? "?# .B

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