Click to Chat

1800-2000-838

+91-120-4616500

CART 0

• 0

MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
```        if y= 1+(a/x-a)+(bx/(x-a)(x-b))+(cx^2/(x-a)(x-b)(x-c))
than show that
dy/dx=y/x[(a/a-x)+(b/b-x)+(c/c-x)].............```
7 years ago

SAGAR SINGH - IIT DELHI
879 Points
```										Dear pradeep,

[a/(x-a)]+1=x/(x-a)
[bx/(x-b)(x-c)]+x/(x-a)=x/(x-a)[b/(x-b)+1]=x2/(x-a)(x-b)
So y={cx^2/ (x-a) (x-b) (x-c)} +x2/(x-a)(x-b)=x2/((x-a)(x-c))[c/(x-c)+1]
y=x3/(x-a)(x-b)(x-c)
logy=3logx-log(x-a)-log(x-b)-log(x-c)
y1/y=3/x+1/(a-x)+1/(b-x)+1/(c-x)
y1/y=[1/x-1/(x-a)]+[1/x-1/x-b]+[1/x-1/x-c]=1/x ( a/a-x + b/ b-x+ c/c-x)

All the best.
Win exciting gifts by answering the questions on Discussion Forum. So help discuss any                                  query on askiitians forum and become an   Elite        Expert        League            askiitian.

Sagar Singh
B.Tech, IIT Delhi

```
7 years ago
510 Points
```										y = 1 + a/(x-a) +bx/(x-a)(x-b) + cx2/(x-a)(x-b)(x-c)
breaking into different  functions

y = 1 +    f(x)1  +       f(x)2       +        f(x)3

f(x)1=a/(x-a)    ,        f(x)2 =bx/(x-a)(x-b)   &   f(x)3 =cx2 /(x-a)(x-b)(x-c)
now
dy/dx= d/dx(1) + d/dx(f(x)1) +d/dx(f(x)2) +d/dx(f(x)3) ....................................1
now separatly differentiatiating f(x)1 , f(x)2  , f(x)3  by taking log
d/dx[log(f(x)1)]  =  d/dx(loga/x-a)
d/dx(f(x)1/f(x)1 = d/dx(loga - log(x-a) )

d/dx(f(x)1)=(-1/x-a)(f(x)1
d/dx(f(x)1) =    -a/(x-a)2
now separatly differentiate each of these and put in eq 1 ,u will get the required result
```
7 years ago
Think You Can Provide A Better Answer ?

## Other Related Questions on Differential Calculus

View all Questions »
• Complete JEE Main/Advanced Course and Test Series
• OFFERED PRICE: Rs. 15,900
• View Details
Get extra Rs. 3,180 off
USE CODE: CHEM20
Get extra Rs. 339 off
USE CODE: CHEM20