Logarithmic Differentiation

The correct option is(C): $x%5E%7B%5Csin%20x%7D%5Cleft(%5Cfrac%7B%5Csin%20x%7D%7Bx%7D%2B%5Clog%20x%20%5Ccos%20x%5Cright)$ .

Given, $y%3Dx%5E%7B%5Csin%20x%7D$
On taking log both sides, we get
$%5Clog%20y%3D%5Csin%20x%20%5Clog%20x$
On differentiating both sides w.r.t. $x$ , we get
$%5Cfrac%7B1%7D%7By%7D%20%5Ccdot%20%5Cfrac%7Bd%20y%7D%7Bd%20x%7D%3D%20%5Csin%20x%20%5Cfrac%7Bd%7D%7Bd%20x%7D%20%5Clog%20x%2B%5Clog%20x%20%5Cfrac%7Bd%7D%7Bd%20x%7D%20%5Csin%20x$
$%5CRightarrow%20%5Cfrac%7B1%7D%7By%7D%20%5Ccdot%20%5Cfrac%7Bd%20y%7D%7Bd%20x%7D%3D%5Csin%20x%20%5Ccdot%20%5Cfrac%7B1%7D%7Bx%7D%2B%5Clog%20x%20%5Ccdot%20%5Ccos%20x$
$%5CRightarrow%20%5Cfrac%7Bd%20y%7D%7Bd%20x%7D%3Dy%5Cleft(%5Cfrac%7B%5Csin%20x%7D%7Bx%7D%2B%5Clog%20x%20%5Ccdot%20%5Ccos%20x%5Cright)$
$%5CRightarrow%20%5Cfrac%7Bd%20y%7D%7Bd%20x%7D%3Dx%5E%7B%5Csin%20x%7D%5Cleft(%5Cfrac%7B%5Csin%20x%7D%7Bx%7D%2B%5Clog%20x%20%5Ccos%20x%5Cright)$

High-Yield Trend

Chapter Questions
1 MCQs

Official Solution

Logarithmic Differentiation

High-Yield Trend

Chapter Questions 1 MCQs

Official Solution

Chapter Questions
1 MCQs