Question

Find the derivatives of the following question w.r.t.x

tan^-1(secx+tanx)

Answer 1

u know what is derivative of tan^(-1)x???

Answer 2

\[\huge D(\tan^{-1} x)=\huge \huge \frac{ 1 }{ 1+x^2 }\]

Answer 3

Yes I know..

Answer 4

so here x= secx+tanx

Answer 5

\[=\huge \frac{ 1 }{ 1+(scex+tanx) ^2} * D(secx+tanx)\]

Answer 6

can u do it now ??

Answer 7

what is derivative of secx ??

Answer 8

Secx*tanx

Answer 9

and that of tanx ??

Answer 10

Sec^2x

Answer 11

sou did it thatz itt

Answer 12

\[\large \frac{ secx*tanx+\sec^2x }{ 1+(secx+tanx)^2 }\]

Answer 13

is it the total answer..??

Answer 14

yeah ....

Answer 15

but the answer is 1/2

Answer 16

u can do it further ..by expanding the square

Answer 17

numerator

Answer 18

keep it as it is ..and come to denominator first

Answer 19

1+sec^2+tan^2+2*tan*sec

Answer 20

when we open the square bracket

Answer 21

sir can you draw it in equation..i am bit confused

Answer 22

lol i m no sir

Answer 23

you are teaching me so ofcourse you are a sir to me

Answer 24

\[1+(secx+tanx)^2=1+(\sec^2x+\tan^2x+2tanx*secx)\]

Answer 25

u got it now ..we are solving denominator first

Answer 26

check my solution

Answer 27

@lanku

Answer 28

@Princer_Jones My question is a bit different..!!

Answer 29

we need to find derivative

Answer 30

Refer to the attachment for some surprising results.

Answer 31

Yes just find the derivative it is 1/2 i gave the expression to it.

Answer 32

@gorv after solving denominator how to proceed to algebra

Answer 33

arc tan means tan inverse

Answer 34

@lanku i already did the solution

Answer 35

tan inverse tan theta =theta.

Answer 36

@Princer_Jones main problem is there that I don't know how I will simplify it..

Answer 37

\[1+\sec^2x+\tan^2x+2tanx*\]

Answer 38

we know that
\[\sec^2x-\tan^2x=1\]

Answer 39

replace one by this ??

Answer 40

sir can you do it from first to last step by step

Answer 41

\[\sec^2x-\tan^2x+\sec^2x+\tan^2x+2tanx*secx\]

Answer 42

@gorv @lanku now check the attachment

Answer 43

lol dont call me sir

Answer 44

@lanku u can go by his approch also that is easy

Answer 45

ok ok

but I still don't get it..please do it from first to last if you have time

Answer 46

I did everything. you just tell me which step you dont understand

Answer 47

after that i don't get anything

Answer 48

@Princer_Jones

Answer 49

I did in a different way, You check my attachment,

Answer 50

ok..thank you

Answer 51

check the attachment, it is the shortest method

Answer 52

but sorry to say I didn't understand that.... where the tan^1 (Secx+tanx) gone??

Answer 53

we calculated sec x+tan x as tan(x/4+pi/2) and you know that tan inverse tan theta is theta.

Answer 54

so the given expression reduces to x/2+pi/4, whose derivative is 1/2

Answer 55

@lanku

Answer 56

yeah i am getting a bit...let me try once..!

Answer 57

ok,,

Answer 58

do i have to assume x=? for this equation to get theta ?

Answer 59

no need of assuming, you just write the steps i wrote in the attachment, first compute tan x+sec x=tan (x/2+pi/4) as i proved it. then just tan inverse (sec x+tan x)=x/2+pi/4

Answer 60

actually our study module is different than yours thatswhy I am getting too much of confusion...but its owk i will find it..thanks for your answer..!!

Answer 61

@lanku I always try to do calculus in methods which are not given in the book. But many times the calculation of 5 minutes is reduced to calculation of 30seconds.Hence I choose always a different way