CBSE Class 12 Math 2023 Delhi Set 1 Solved Paper

Question : 6 of 38

Marks: +1, -0

The derivative of

x^{2 x}

w.r.t.

x

is:

Solution:

y\;=x^{2 x}

\log y\;=2 x \log x

\;{d}/{d x} \log y\;=\;{d}/{d x} 2 x \log x

\;{1}/{y} \;{d y}/{d x}\;=2 [x \;{d}/{d x} \log x+\log x \;{d}/{d x} x]

\;{d y}/{d x}\;=2 y [x × \;{1}/{x}+\log x]

\;{d y}/{d x}\;=2 x^{2 x}[1+\log x]

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