Difference between revisions of "Differentiation Rules"
Aimesolver (talk | contribs) (→Derivatives of Trig Functions) |
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'''Derivative of Sine''' | '''Derivative of Sine''' | ||
If <math>y(x) = \sin x</math>, then <math>\frac{dy}{dx} = \cos x</math>. | If <math>y(x) = \sin x</math>, then <math>\frac{dy}{dx} = \cos x</math>. | ||
+ | |||
+ | '''Derivative of Cosine''' | ||
+ | If <math>y(x) = \cos x</math>, then <math>\frac{dy}{dx} = -\sin x</math>. | ||
+ | |||
+ | '''Derivative of Tangent''' | ||
+ | If <math>y(x) = \tan x</math>, then <math>\frac{dy}{dx} = \sec^2 x</math>. Note that this follows from the Quotient Rule. |
Revision as of 10:46, 18 November 2010
Differentiation rules are rules (actually, theorems) used to compute the derivative of a function in calculus. In what follows, all functions are assumed to be differentiable.
Basic Rules
Derivative of a Constant:
If is a constant function then
.
Sum Rule:
If then
.
Product Rule:
If then
.
Quotient Rule:
If then
.
Chain Rule:
If then
.
Power Rule:
If then
. For integer
this is just a consequence of the product and quotient rules and induction, but it can also be proven for all real numbers
, e.g. by using the extended Binomial Theorem.
Derivatives of Trig Functions
Derivative of Sine
If , then
.
Derivative of Cosine
If , then
.
Derivative of Tangent
If , then
. Note that this follows from the Quotient Rule.