If y=sinlogexthen x2d2ydx2+xdydxis equal to
sinlogex
coslogex
y2
-y
Explanation for the correct option:
y=sinlogex
Step 1: Differentiating with respect to x both sides :
dydx=coslogex×1x=coslogexx
So,dydx=coslogexx
Step 2: Using Quotient rule and again differentiating with respect to x both sides :
d2ydx2=x-sinlogex×1x-coslogexx2=-coslogex-sinlogexx2
So, d2ydx2=-coslogex-sinlogexx2
x2d2ydx2=-coslogex-sinlogex=-xdydx-y
⇒x2d2ydx2+xdydx=-y
Hence, Option (D) is the correct answer.