If y = x^{(x^x)},then frac{dy}{dx} = | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given $y = x^{(x^x)}$.Taking natural logarithm on both sides: $\log y = x^x \log x$.Differentiating both sides with respect to $x$:$\frac{1}{y} \f

Vedclass · Accepted Answer

$y[x^x(\log_e x + 1)\log x + x^{x-1}]$

Vedclass · Answer

(C) Given $y = x^{(x^x)}$.Taking natural logarithm on both sides: $\log y = x^x \log x$.Differentiating both sides with respect to $x$:$\frac{1}{y} \frac{dy}{dx} = \frac{d}{dx}(x^x) \cdot \log x + x^x \cdot \frac{d}{dx}(\log x)$.We know that if $z = x^x$,then $\log z = x \log x$,so $\frac{1}{z} \frac{dz}{dx} = 1 \cdot \log x + x \cdot \frac{1}{x} = \log x + 1$.Thus,$\frac{dz}{dx} = x^x(\log x + 1)$.Substituting this back: $\frac{1}{y} \frac{dy}{dx} = [x^x(\log x + 1)] \log x + x^x \cdot \frac{1}{x}$.Since $x^x \cdot \frac{1}{x} = x^{x-1}$,we have:$\frac{dy}{dx} = y [x^x(\log x + 1)\log x + x^{x-1}]$.

If $y = x^{(x^x)}$,then $\frac{dy}{dx} = $

Similar Questions

If $y=\sqrt{e^{\sqrt{x}}}$,then $\frac{d y}{d x}=$

$y=\frac{\sqrt[3]{1+3 x} \sqrt[4]{1+4 x} \sqrt[5]{1+5 x}}{\sqrt[7]{1+7 x} \sqrt[8]{1+8 x}}$. Then $\frac{d y}{d x}$ at $x=0$ is

If $y = \frac{e^{2x} \cos x}{x \sin x}$,then $\frac{dy}{dx} = $

If $y = ((x+1)(4x+1)(9x+1) \ldots (n^2x+1))^2$,then $\frac{dy}{dx}$ at $x=0$ is

If $x^y=y^{\sin x}(\tan x)^{\cos x}$, then $\left(\log x-\frac{\sin x}{y}\right) \frac{d y}{d x}=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module