IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

kasirajan.1990

find dy/dx of the following 1) xy=e^(x-y)
2) find the derivative of function given by:
(1+x) (1+x²) (1+x⁴) (1+x⁸) and hence find f'(1)

utkarsh123

rate me then i will tell

neeraj_agarwal_1990

1) x dy/dx + y= e^(x-y) . (1- dy/dx)
now u can solve

2) 1+ x+ x^2 + x^4 + x^8 + x^15
now u can solve

subs

1 >>>> (e^x[x-1])/(x^2(e^y+ye^y))

2>>>>1+2x+4x^3+8x^7+15x^14

vinod

kasirajan.1990 solution for the frst quen ..

EDITED

vinod

kasirajan.1990 solution for the second quen .. plzz tell me some thing is wrong

f¹= 2 x 2 x 2 x 2 [ 1/2 + 2/2 + 4/2 + 8/2 ]

= 16 x [7.5]

= 120 .

vasanth

dy/dx = (1 + x.x)(1+x.x.x.x)(1+x.x....8times) +(1+x)( 2x)(1+x^4)(1+x^8) + (1+x)(1+x^2)(4x^3)(1+x^8) + (1+x)(1+x^2)(1+x^4)(8x^7)

x = 1

dy/dx = 8 + 16 + 32 + 64 = 120

do rate me!

cheers!

Arjun

hiiiiiiii.........

now for da second question.........

f(x) = (1+x)(1+x²)(1+x⁴)(1+x⁸)

f(x)=1/1-x *(1-x)(1+x)(1+x²)(1+x⁴)(1+x⁸)

u'll get a+b*a-b=a²-b²form........go on simplifyin.......

finally.......u'll get

f(x)=1-x¹⁶/1-x

d/dx=1-x(-16x¹⁵)-(-1)/(1-x)²

the differential is equal to......

(1-x)(-16x¹⁵)+1/(1-x)²

here f^'(1)does not exist bcoz......in da denominateor u get 0..........

hope u got it!!!!

Arjun

hey.......i guess m gettin a wrong answer.........but da method is ryt,na??????????????

plzzzzzzzzzzzzz help!!!!!!

Arjun

ne body.help.........

vinod

The mthod is absolutely right !! and fast and easy tooooo....but i toooo am wondering y itz giving wrong ans

amar.gupta

Dear,

I think you have got the ans. of both of your question.

however vinod , you have done a slight mistake while solving the que.1 .

it should be (dy/dx)[(1+y)/y] =(x-1)/x

and arjun as you have multiplied and divided by (x-1) but you can divide the expression by (x-1) only when x can not be 1 . but here x can be 1 .

that's why you have find this kind of expression in the end .

it is not defined at x=1 but the results will be true for all other x.

vinod

Thank u sir,

I have edited the post ..

ananya.123

second answer is 130??

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