Question originally asked by

**Chantey Peter**.

__First lets us look at the differentiation of Trigonometric functions:__
Since, I have applied learning/remembering by pattern in this
Mnemonic Device. From this I have developed simple rules.

**Rules derived from pattern**.

1. If there is
C in front : then negative (-) on the
backside.

Eg. Derivative of cosx = - sin x ; Since there is C in
Cosx so negative on the backside.

2. If there is
C in the last letter of the front word : then there are two items.

Eg. Derivative of secx = secx.tanx ; Since there is C
at last in seCx so there are two items as secx and tanx.

3. If there
are 2 terms ; one must be itself.

**Now, let’s talk the individuals**:

a. Derivative of
Sinx = cosx ; you should and would
remember this automatically.

If
not: remember that there is a formula where sin^2x + cos^2x = 1. So sin and cos
comes together.

b. Derrivative
of Cosx = - Sinx ; Sin and cos go on exchange according to a. And Negative sign
according to rule number 1.

c. Derrivative
of tanx = sec^2x ; Do you remember the formula sec^2x + tan^2x = 1. From this
you can remember that sec and tanx comes together.

d. Derivative
of cosecx = - cosecx.cotx ; negative is according to rule 1. And, there are 2
terms according to rule 2. Now, Remember there are 2 terms, cosecx and cotx :
cosecx is OK since it is in question ( analyse the pattern ) and Cotx from the
last.

e. Derivative of
secx = secx.tanx ; two terms according to rule 2. Secx : since it is in the
question, tanx: last from sin cos and tan. Just opposite of cosecx. ( analyse the
pattern )

f.
Derivative of cotx = -cosec^2x ; Negative is according to rule number 1. And
since tanx had sec^2x ; cotx must have cosec^2x. ( anaylze the pattern )

__Now let’s remember Integration of Trigonometric Functions.__**Rules derived from pattern**

1. If C in
second part then negative on the result. ( opposite of derivative )

2. If there is
C at last then there are two terms in result. ( same as in derivative )

3. If there
are two terms one must be itself.

**Now, let’s talk the individuals**:
a. Integration
of sinx = - cosx + c ; Negative for rule
1. remember the relation of sin and cos.

b. Integration
of cosx = sinx + c ; Relation of sin and cos.

c. Integration
of tanx = -ln (cosx) + c ; If you know the rule of integration then you will

d. Integration
of cosecx = - ln ( cosecx + cotx ) + c ; Two terms according to rule 2. Negative
according to rule 1. Since there are two terms one is cosec and other is of last cot. Same as
in Derivative. Read the pattern.

e. Integration
of secx = ln ( secx + tanx ) + c ; Two terms according to rule number 2. Since
there are two terms one must be itself ( rule no. 3 ). Other is last one i.e.
tanx. Read the pattern.

f.
Integration of cotx = ln ( sinx ) + c ; Since tan had
cos; cot has sin. Read the pattern.

Since it is based on reading the pattern, you may get confused by reading this. But use there on some places then you will surely remember the pattern. Also, the best way to remember maths formula is to practice !!!

Since it is based on reading the pattern, you may get confused by reading this. But use there on some places then you will surely remember the pattern. Also, the best way to remember maths formula is to practice !!!

really useful!

ReplyDeleteI am glad to hear this.

DeleteJust awesome,

ReplyDeletethank you

great to hear that.

Deletesupeb !thanks a lot !post more there are many more formulas of integration and diffrention which usually confuses

ReplyDeletethank you! :) great mnemonics. hope you could do more!

ReplyDeleteit's helpful

ReplyDeletevery useful

ReplyDeleteVery helpful! One thing I noticed: sec^2x + tan^2x = 1. is wrong. It should be sec^2x = tan^2x + 1.

ReplyDeletelol its awesome work ...great job

ReplyDeletegreat job....

ReplyDeleteyup . it should be

ReplyDeletesec^2x = tan^2x + 1.