Find d y d x if, : y= ( x) - Vidyadip

Question

Find $\frac{d y}{d x}$ if, :
$
y=\log (\log x)
$

✓

Answer

Given $y=\log (\log x)$
Let $u =\log x$
Then $y =\log u$
$
\therefore \frac{d y}{d u}=\frac{d}{d u}(\log u)
$
$
\begin{aligned}
& =\frac{1}{u}=\frac{1}{\log x} \\
& \text { and } \frac{d u}{d x}=\frac{d}{d x}(\log x)=\frac{1}{x} \\
& \therefore \frac{d y}{d x}=\frac{d y}{d u} \cdot \frac{d u}{d x}=\frac{1}{\log x} \times \frac{1}{x} \\
& =\frac{1}{x \log x} \text {. } \\
\end{aligned}
$

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.(2 Marks)" from Differentiation (p-1)→Differentiation (p-1) — 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

A car firm has $2$ cars, which are hired out day by day. The number of cars hired on a day follows a Poisson distribution with a mean of $1.5.$ Find the probability that
(i) no car is used on a given day.
(ii) some demand is refused on a given day, given $e^{-1.5} = 0.2231.$

Find the accumulated value of annuity due of $\text{₹} 1,000$ p.a. for $3$ years at $10 \%$ p.a. compounded annually. [Given: $(1.1)^3=1.331$ ]

Rewrite the following statements without using conditional:
[Hint: P → q ≡ ~p ∨ q]
(i) If price increases, then demand falls.
(ii) If demand falls, then the price does not increase.

For each of the following matrices, find its transpose and state whether it is symmetric, skew-symmetric or neither:
$\left[\begin{array}{ccc}2 & 5 & 1 \\ -5 & 4 & 6 \\ -1 & -6 & 3\end{array}\right]$

Given that $\sum p_0q_0 = 220, \sum p_0q_1 = 380, \sum p_1q_1 = 350$ is Marshall-Edgeworth’s Price Index Number is $150$, find Laspeyre’s Price Index Number.

Find $\frac{d y}{d x}$ if, :
$
x=2 a t^2, y=a t^4
$

Check whether following matrices are invertible or not: $\left[\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right]$

Find the mean of the number of heads in three tosses of a fair coin.

Using the truth table, prove the following logical equivalences:
~p ∧ q ≡ (p ∨ q) ∧ ~p

Given that $\sum p_0q_0 = 130, \sum p_1q_1 = 140, \sum p_0q_1 = 160$, and $\sum p_1q_0 = 200$, find Laspeyare’s, Passche’s, Dorbish-Bowely’s and Mashall-Edegeworth’s Price Inbox Numbers.