If , #y=sqrt(x/a)-sqrt(a/x)# So, Prove that ?? #2xy(dy/dx)= x/a-a/x#
If , #y=sqrt(x/a)-sqrt(a/x)# So, Prove that #?#
#2xydy/dx= x/a-a/x#
If ,
3 Answers
Given:
Differentiating:
Multiply both sides by2xy:
Substitute
Please observe that the right side is the pattern
Kindly see a Proof in Explanation.
Explanation:
We have,
Diff.ing w.r.t.
Multiplying by
Again multiplying by
We seek to show that:
#2xydy/dx= x/a-a/x# where#y=sqrt(x/a)-sqrt(a/x)#
Squaring the expression, and then expanding, we get:
# y^2 = (sqrt(x/a)-sqrt(a/x))^2 #
# \ \ \ \= (sqrt(x/a))^2 - 2(sqrt(x/a))(sqrt(a/x)) + (sqrt(a/x))^2#
# \ \ \ \= x/a - 2 + a/x #
Differentiating Implicitly, we get
# 2y dy/dx = 1/a -a/x^2 #
Finally, multiplying by
# 2xy dy/dx = x/a -a/x \ \ \ # QED