wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If yyy=x+x+x.... then dydx is equal to

A
yx+1yx1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
yxy+x
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
x+y+1yx
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
yx+1y+x
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B yx+1yx1
yyy...=x+x+x...+[1]
Squaring both Sides,

yyyy...=x+x+x+x...+
From [1]

yx+x+x...+=x+x+x+x...+

y=x+2x+x+x...+

yx=2x+x+x...+[2]

Squaring both Sides,

(yx)2=4(x+x+x+x...+)

From [2]
y2+x22yx=4(x+(yx)2)

y2+x22yx=4(x2+y2)

Multiplying 2,

2y2+2x24yx=4(x+y)

Differentiating with respect to x,
4ydydx+4x4y4xdydx=4+4dydx

dydx(4y4x4)=4y4x+4

dydx(yx1)=yx+1

dydx=yx+1yx1

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Properties of Inequalities
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon