Download App

Differentiation — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDifferentiation1 Mark
MCQ
$\frac{\text{d}}{\text{dx}}\bigg[\log\bigg\{\text{e}^\text{x}\Big(\frac{\text{x}-2}{\text{x}+2}\Big)^\frac{3}{4}\bigg\}\bigg]$ equals:
  • ✓
    $\frac{\text{x}^2-1}{\text{x}^2-4}$
  • B
    $1$
  • C
    $\frac{\text{x}^2+1}{\text{x}^2-4}$
  • D
    $\text{e}^\text{x}\frac{\text{x}^2-1}{\text{x}^2-4}$
✓

Answer

Correct option: A.
$\frac{\text{x}^2-1}{\text{x}^2-4}$
Let, $\text{y}=\frac{\text{d}}{\text{dx}}\bigg[\log\bigg\{\text{e}^\text{x}\Big(\frac{\text{x}-2}{\text{x}+2}\Big)^\frac{3}{4}\bigg\}\bigg]$
$\Rightarrow\text{y}=\frac{\text{d}}{\text{dx}}\Big[\text{x}\log\text{e}+\frac{3}{4}\log\Big(\frac{\text{x}-2}{\text{x}+2}\Big)\Big]$
$\Rightarrow\text{y}=\frac{\text{d}}{\text{dx}}\Big[\text{x}+\frac{3}{4}\log\Big(\frac{\text{x}-2}{\text{x}+2}\Big)\Big]$
$\Rightarrow\frac{\text{d}}{\text{dx}}=1+\frac{3}{4\Big(\frac{\text{x}-2}{\text{x}+2}\Big)}\times\frac{(\text{x}+2)\times1-(\text{x}-2)\times1}{(\text{x}+2)^2}$
$\Rightarrow\frac{\text{d}}{\text{dx}}=1+\frac{3(\text{x}+2)}{4(\text{x}-2)}\times\frac{\text{x}+2-\text{x}+2}{(\text{x}+2)^2}$
$\Rightarrow\frac{\text{d}}{\text{dx}}=1+\frac{3(\text{x}+2)}{4(\text{x}-2)}\times\frac{4}{(\text{x}+2)}$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=1+\frac{3}{(\text{x}^2-4)}$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{\text{x}^2-4+3}{\text{x}^2-4}$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{\text{x}^2-1}{\text{x}^2-4}$

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 "MCQ" from Differentiation→Differentiation — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Every invertible function is:
→
Considering only the principal values of inverse functions, the set$ A=\left\{x \geq 0 / \tan ^{-1}(2 x)+\tan ^{-1}(3 x)=\frac{\pi}{4}\right\} $
→
If $x=e^\theta(\sin \theta-\cos \theta), y=e^\theta(\sin \theta+\cos \theta)$, then $\frac{d y}{d x}$ at $\theta=\frac{\pi}{4}$ is
→
If the angle between the two lines given by $a x^2+2 h x y+b y^2+2 g x+2 f y+c=0$ is $\frac{\pi}{4}$, then the constants $a , b , h , g , f , c$ are related by
→
The value of $\int_2^3 \frac{x+1}{x^2(x-1)} d x$ is
→
If p.m.f. of a d.r.v. $X$ takes values $0,1,2,3, \ldots$ which probability $P(X=x)=k(x+1) .5-x$, where $k$ is a constant, then $P(X=0)=$
→
The value of $f(0)$, so that the function $\text{f(x)}=\frac{(27-2\text{x})^\frac{1}{3}-3}{9-3(243+5\text{x})^\frac{1}{5}}$ is continuous, is given by:
→
The area bounded by the parabola $y^2=32 x$ the $X$-axis and the latus rectum is ____ sq.units
→
Equation of a line passing through point $(1,2,3)$ and parallel to XZ-plane is
→
The differential equation of all circles having their centres on the line y = 5 and touching the X-axis is
→