Find d y d x , if y =[ ( ( x ))]^2 - Vidyadip

Question

Find $\frac{ d y}{ d x}$, if $y =[\log (\log (\log x ))]^2$

✓

Answer

$y=[\log (\log (\log x))]^2$

Differentiating both sides w.r.t. $x$, we get
$ \frac{ d y}{ d x}=\frac{ d }{ d x}[\log (\log (\log x))]^2$
$=2[\log (\log (\log x))] \times \frac{ d }{ d x}[\log (\log (\log x))]$
$=2[\log (\log (\log x))] \times \frac{1}{\log (\log x)} \times \frac{ d }{ d x}[\log (\log x)]$
$=2[\log (\log (\log x))] \times \frac{1}{\log (\log x)} \times \frac{1}{\log x} \times \frac{ d }{ d x}(\log x)$
$=2[\log (\log (\log x))] \times \frac{1}{\log (\log x)} \times \frac{1}{\log x} \times \frac{1}{x}$
$\therefore \frac{ d y}{ d x}=\frac{2[\log (\log (\log x))]}{x(\log x)(\log (\log x))} $

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(3 Marks)" from Question Bank [2022]→Question Bank [2022] — all question types→Maths (commerce) STD 12 Commerce / Arts question papers→Maharashtra Board STD 12 Commerce / Arts question papers→Maharashtra Board question paper generator→

Similar questions

If X has Poisson distribution with $m = 1$, then find $P(X \leq 1)$ given $e^{−1} = 0.3678$

Find the future value after 2 years if an amount of ₹ 12,000 is invested at the end of every half-year at $12 \%$ p.a. compounded half-yearly. [Given: $(1.06)^4=1.2625$ ]

If $A=\left[\begin{array}{cc}2 & 1 \\ 0 & 3 \\ 1 & -1\end{array}\right]$ and $B=\left[\begin{array}{ccc}0 & 3 & 5 \\ 1 & -7 & 2\end{array}\right]$, then verify $(B A)^{\top}=A^{\top} B^{\top}$

Evalute : $\int \frac{x^3}{16 x^8-25} d x$

If $\sum p_0q_0 = 140, \sum p_0q_1 = 200, \sum p_1q_0 = 350, \sum p_1q_1 = 460,$ find Laspeyre’s Paasche’s Dorbish-Bowley’s and Marshall- Edgeworth’s Price Index Numbers.

Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers. Find E(X).

If $X$ has Poisson distribution with parameter $m$, such that
$\frac{P(X=x+1)}{P(X=x)}=\frac{m}{x+1}$
find probabilities $P(X=1)$ and $P(X=2)$, when $X$ follows Poisson distribution with $m =2$ and $P ( X =0)=0.1353$.

Find $\frac{d y}{d x}$ if, :
$
y=e^{x^x}
$

The probability distribution of a discrete r.v. X is as follows.

X	1	2	3	4	5	6
P(X=x)	K	2K	3K	4K	5K	6K

(i) Determine the value of k.
(ii) Find P(X ≤ 4), P(2 < X < 4), P(X ≥ 3).

Solve the following differential equations : $\frac{d y}{d x}+2 x y=x$