Differentiation Question 95
Question: If $ u={{(x^{2}+y^{2}+z^{2})}^{3/2}} $ , then $ {{( \frac{\partial u}{\partial x} )}^{2}}+{{( \frac{\partial u}{\partial y} )}^{2}}+{{( \frac{\partial u}{\partial z} )}^{2}}= $
[EAMCET 1996]
Options:
A) 9u
B) $ 9{u^{4/3}} $
C) $ 9u^{2} $
D) $ {u^{4/3}} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \frac{\partial u}{\partial x}=\frac{3}{2}{{(x^{2}+y^{2}+z^{2})}^{1/2}}.2x $
$ \therefore $ $ {{( \frac{\partial u}{\partial x} )}^{2}}=\frac{9}{4}(x^{2}+y^{2}+z^{2})4x^{2} $ = $ 9x^{2}(x^{2}+y^{2}+z^{2}) $
$ \therefore $ $ {{( \frac{\partial u}{\partial x} )}^{2}}+{{( \frac{\partial u}{\partial y} )}^{2}}+{{( \frac{\partial u}{\partial z} )}^{2}} $
= $ 9(x^{2}+y^{2}+z^{2})(x^{2}+y^{2}+z^{2}) $
= $ 9{{(x^{2}+y^{2}+z^{2})}^{2}} $ = $ 9.{u^{4/3}} $ .
BETA
