Test Index

CBSE Class 12 Math 2023 Delhi Set 1 Solved Paper

© examsnet.com
Question : 6 of 38
Marks: +1, -0
The derivative of x2xx^{2x} w.r.t. xx is:
Solution:     👈: Video Solution
y  =x2xy\;=x^{2x}
log⁡y  =2xlog⁡x\log y\;=2x\log x
  ddxlog⁡y  =  ddx2xlog⁡x\;\frac{d}{dx}\log y\;=\;\frac{d}{dx}2x\log x
  1y  dydx  =2[x  ddxlog⁡x+log⁡x  ddxx]\;\frac{1}{y}\;\frac{dy}{dx}\;=2\left[x\;\frac{d}{dx}\log x+\log x\;\frac{d}{dx}x\right]
  dydx  =2y[x×  1x+log⁡x]\;\frac{dy}{dx}\;=2y\left[x\times\;\frac{1}{x}+\log x\right]
  dydx  =2x2x[1+log⁡x]\;\frac{dy}{dx}\;=2x^{2x}\left[1+\log x\right]
© examsnet.com
Go to Question:
Prev Question
Next Question