Question

The value of ddxx2x=

• A. (A) 2x2log⁡x
• B. (B) x22(1+log⁡x)
• C. (C) x2x
• D. (D) 2x2x[1+log⁡x]

Answer 1

Answer: (D)

(D) 2x2x[1+log⁡x]

Answer 2

Explanation:
Given:ddxx2xConcept:log⁡xn=nlog⁡xddx[log⁡x]=1xLet, y=x2xTaking log on both the sides, we getlog⁡y=log⁡(x2x)=2xlog⁡x(∵log⁡xn=nlogx)Now, taking derivatives,ddx[log⁡y]=2{ddx[x]log⁡x+ddx[log⁡x]x}1ydydx=2log⁡x+x⋅1x⇒dydx=2y[1+log⁡x]⇒dydx=2x2x1+log⁡xHence, the correct option is (D).