Differentiate the following w.r.t. x: [ ( ^5) ] - Vidyadip

Question

Differentiate the following w.r.t. x:
$\log\big[\log(\log\text{x}^5)\big]$

✓

Answer

Let $\text{y}=\log\big[\log(\log\text{x}^5)\big]$
$\therefore\ \frac{\text{dy}}{\text{dx}}=\frac{\text{d}}{\text{dx}}\log\big[\log(\log\text{x}^5)\big]$
$=\frac{1}{\log\log\text{x}^5}\cdot\frac{\text{d}}{\text{dx}}\big(\log\cdot\log\text{x}^5\big)$
$=\frac{1}{\log\log\text{x}^5}\cdot\frac{1}{\log\text{x}^5}\cdot\frac{\text{d}}{\text{dx}}\log\text{x}^5$
$=\frac{1}{\log\log\text{x}^5}\cdot\frac{1}{\log\text{x}^5}\cdot\frac{\text{d}}{\text{dx}}(5\log\text{x})$
$=\frac{5}{\text{x}\cdot\log(\log\text{x}^5)\cdot\log(\text{x}^5)}$

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 "3 Marks Question" from CONTINUITY AND DIFFERENTIABILITY→CONTINUITY AND DIFFERENTIABILITY — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Write the angle between the curves $y^2 = 4x$ and $x^2 = 2y - 3$ at the point $(1, 2)$.

Check the commutativity and associativity of the following binary operations:
'*' on Q defined by $a * b = ab^2$ for all $a, b \in Q.$

Check the commutativity and associativity of the following binary operations:
'*' on N defined by $a * b = 2^{ab}$ for all $a, b \in N.$

Show that the relation $R$ in the set $A$ of points in a plane given by $R = \{(P, Q) :$ distance of the point $P$ from the origin is same as the distance of the point $Q$ from the origin$\}$, is an equivalence relation. Further, show that the set of all points related to a point $P \ne (0, 0)$ is the circle passing through $P$ with origin as centre.

Solve the following equation for x:
$\tan^{-1}\Big(\frac{\text{x}-2}{\text{x}-4}\Big)+\tan^{-1}\Big(\frac{\text{x}+2}{\text{x}+4}\Big)=\frac{\pi}{4}$

Reduce the equation of the following planes to intercept from and find the intercepts on the coordinate axes:
4x + 3y - 6z - 12 = 0

Evaluate the following definite integrals:
$\int_{0}^\limits{\frac{\pi}{2}}\text{x}^2\cos2\text{x}\text{ dx}$

Evaluate the following integrals:
$\int\tan^\frac{3}{2}\text{x}\sec^2\text{x dx}$

Without using the derivative, show that the function f(x) = |x| is

Strictly increasing in $(0,\infty)$
Strictly decreasing in $(-\infty,0)$

Let '*' be a binary operation on N defined by a * b = 1.c.m. (a, b) for all $\text{a, b}\in\text{N}.$
Check the commutativity and associativity of '*' on N.