frac{d}{dx} log(log x) = | vedclass

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

Question

(C) To find the derivative of $\log(\log x)$ with respect to $x$,we use the chain rule.Let $y = \log(\log x)$.Applying the chain rule,$\frac{dy}{dx} =

Vedclass · Accepted Answer

$(x \log x)^{-1}$

Vedclass · Answer

(C) To find the derivative of $\log(\log x)$ with respect to $x$,we use the chain rule.Let $y = \log(\log x)$.Applying the chain rule,$\frac{dy}{dx} = \frac{d}{d(\log x)} \log(\log x) \cdot \frac{d}{dx} \log x$.Since $\frac{d}{du} \log u = \frac{1}{u}$ and $\frac{d}{dx} \log x = \frac{1}{x}$,we get:$\frac{dy}{dx} = \frac{1}{\log x} \cdot \frac{1}{x} = \frac{1}{x \log x}$.This can be written as $(x \log x)^{-1}$.Therefore,the correct option is $C$.

$\frac{d}{dx} \log(\log x) =$

Similar Questions

Let $f$ be a differentiable function such that $f(1) = 2$ and $f'(x) = f(x)$ for all $x \in R$. If $h(x) = f(f(x))$,then $h'(1)$ is equal to

Let $f : R \rightarrow R$ be defined as $f(x) = x^{3} + x - 5$. If $g(x)$ is a function such that $f(g(x)) = x, \forall x \in R$,then $g^{\prime}(63)$ is equal to

For some constants $a$ and $b$,find the derivative of $(x-a)(x-b)$.

If $f(x) = \frac{1}{\sqrt{x^2 + a^2} + \sqrt{x^2 + b^2}}$,then $f'(x)$ is equal to

If $r = [2\phi + \cos^2(2\phi + \pi/4)]^{1/2}$,then what is the value of the derivative $dr/d\phi$ at $\phi = \pi/4$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module