BPSC 44th Exam Prelims 2002 Solved Paper

Question : 119 of 150

Marks: +1, -0

If y = |x| (x ≠ 0) then dy/dx is –

Solution:

y=|x|

y=√{x^{2}}=(x^{2})^{\;{1}/{2}}

\;{d y}/{d x}=\;{1}/{2}(x^{2})^{\;{1}/{2}-1} ⋅ \;{d}/{d x}(x^{2})

[ ∵

By chain rule

]

\;{d y}/{d x}=\;{1}/{2}(x^{2})^{-\;{1}/{2}} ⋅ 2 x

=\;{x}/{(x^{2})^{\;{1}/{2}}}=\;{x}/{√{x^{2}}}

\;{d x}/{d x}=\;{x}/{|x|}

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