Question

If $y=\frac{e^x\log x}{x^2}$, then $dy/dx$ is equal to ?

• A. $e^x[1+(x+2)\log x]/x^4$
• B. $e^x[1+(x-2)\log x]/x^4$
• C. $e^x[1–(x–2)\log x]/x^3$
• D. $e^x[1+(x–2)\log x]/x^3$

Answer 1

The correct option is D

$e^x[1+(x–2)\log x]/x^3$

Step 1: Given Function

The Given function is $y=\frac{e^x\log x}{x^2}$

Step 2: Differentiate the given function with respect to $x$

$$\begin{gathered} dy/dx=[x^2(d/dx)(e^x\log x)–(e^x\log x\left)2x\right]/x^4 \\ dy/dx=[x^2(e^x\log x+e^x.1/x)–(e^x\log x\left)2x\right]/x^4 \\ dy/dx=e^x[x^2\log x+x–2x\log x]/x^4 \\ dy/dx=e^x[x\log x+1–2\log x]/x^3 \\ dy/dx=e^x[1+(x–2)\log x]/x^3 \end{gathered}$$

Therefore the option (D) is correct.