Question

If y=lognx, where logn means loge loge loge .....(repeated n times), then xlogx log2x log3x....log n-1 xlognx $\frac{dy}{dx}$ is equal to :

• A. log x
• B. x
• C. 1
• D. lognx

Answer 1

Answer: (D)

lognx

Answer 2

The correct answer is option (D) : lognx
$\because$ $y=log^n x$
On differentiating w.r.t $x$, we get,
$x\,log\,x\,log^2x\,log^3x.....log^{n-1}xlog^nx\frac{dy}{dx}$
$\frac{x\,log\,x\,log^2x\,log^3x.....log^{n-1}xlog^nx.1}{x\,log\,x\,log^2x\,log^3x.....log^{n-1}x}$

The correct option is (D):
$= log^nx$