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Basic Differentiation Formulas 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

..B . .B

œ ! (-?) œ -

. .B

(? „ @) œ

.@ .B

Product Rule

. .B

.@ (?@Ñ œ ? .B @

.? .B

Quotient Rule

. .B

( ?@ ) œ

Chain Rule

.C .B

œ

(If + = / )

(If + 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 ? .B # @

.C .? .? .B

. .B

B8 œ 8B8"

. .B

?8 œ 8?8"

. .B

+B œ (ln +) +B

. .B

+? œ (ln +) +?

. .B

/B œ /B

. .B

/? œ /?

. .B

log+ B œ

. .B

log+ ? œ

. .B

ln B œ

. .B

ln ? œ

. .B

sin B œ cos B

. .B

sin ? œ cos ?

. .B

cos B œ  sin B

. .B

cos ? œ  sin ?

. .B

tan B œ sec# B

. .B

tan ? œ sec# ?

. .B

cot B œ  csc# B

. .B

cot ? œ  csc# ?

. .B

sec B œ sec B tan B

. .B

sec ? œ sec ? tan ?

. .B

csc B œ  csc B cot B

. .B

csc ? œ  csc ? cot ?

. .B

sin" B œ

. .B

sin" ? œ

. .B

arcsin B œ

. .B

arcsin ? œ

. .B

tan" B œ

. .B

tan" ? œ

. .B

1 (ln +) B

1 B

1 È"B#

arctan B =

1 "B#

. .B

.? .B

.? .B

.? .B .? 1 (ln +) ? .B

1 .? ? .B

.? .B .? .B

.? .B

1 È"?#

arctan ? =

.? .B .? .B

.? .B

.? 1 "?# .B

.? .B


Differentiation formulae  

This is a list of basic differentiation formula

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