enEnglishguગુજરાતી
JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If \(f\left( x \right) = {\sin ^{ - 1}}\left( {\frac{{2 \times {3^x}}}{{1 + {9^x}}}} \right)\), then \(f'(-\frac {1}{2})\) equals
- A \(\sqrt 3\, {\log _e}\,\sqrt 3 \)
- B \( - \sqrt 3 \,{\log _e}\,\sqrt 3 \)
- C \( - \sqrt 3 \,{\log _e}\,3\)
- D \( \sqrt 3 \,{\log _e}\,3\)
Answer & Solution
Correct Answer
(A) \(\sqrt 3\, {\log _e}\,\sqrt 3 \)
Step-by-step Solution
Detailed explanation
Since \(f\left( x \right) = \sin \left( {\frac{{2 \times {3^x}}}{{1 + {9^x}}}} \right)\) Suppose \({3^x} = \tan t\) \( \Rightarrow f\left( x \right) = {\sin ^{ - 1}}\left( {\frac{{2\tan t}}{{1 + {{\tan }^2}t}}} \right)\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let \(z \in C\) be such that \(\left| z \right| < 1\). If \(w = \frac{{5 + 3z}}{{5\,\left( {1 - z} \right)}}\), thenJEE Mains 2019 Hard
- The length of the latus rectum and directrices of a hyperbola with eccentricity e are 9 and \(\mathrm{x}= \pm \frac{4}{\sqrt{3}}\), respectively. Let the line \(y-\sqrt{3} \mathrm{x}+\sqrt{3}=0\) touch this hyperbola at \(\left(\mathrm{x}_0, \mathrm{y}_0\right)\). If \(\mathrm{m}\) is the product of the focal distances of the point \(\left(\mathrm{x}_0, \mathrm{y}_0\right)\), then \(4 \mathrm{e}^2+\mathrm{m}\) is equal to ...........JEE Mains 2024 Hard
- Let \(M =\left[\begin{array}{cc}0 & -\alpha \\ \alpha & 0\end{array}\right]\), where \(\alpha\) is a non-zero real number an \(N =\sum\limits_{ k =1}^{49} M ^{2 k }\). If \(\left( I - M ^{2}\right) N =-2 I\), then the positive integral value of \(\alpha\) isJEE Mains 2022 Hard
- Let \(\vec{p}=2 \hat{i}+3 \hat{j}+k\) and \(\vec{q}=\hat{i}+2 \hat{j}+k\) be two vectors. If \(a\) vector \(\vec{r}=(a \hat{i}+\beta \hat{j}+\gamma k)\) is perpendicular to each of the vectors \((\vec{p}+\bar{q})\) and \((\vec{p}-\vec{q})\), and \(|\vec{r}|=\sqrt{3}\), then \(|\alpha|+|\beta|+|\gamma|\) is equal to \(.....\)JEE Mains 2021 Hard
- Let \(\alpha, \beta\) be the roots of the quadratic equation \(x^2+\sqrt{6} x+3=0\). Then \(\frac{\alpha^{23}+\beta^{23}+\alpha^{14}+\beta^{14}}{\alpha^{15}+\beta^{15}+\alpha^{10}+\beta^{10}}\) is equal toJEE Mains 2023 Hard
- Given : \(f(x)=\left\{\begin{array}{ccc}{x} & {,} & {0 \leq x < \frac{1}{2}} \\ {\frac{1}{2}} & {,} & {x=\frac{1}{2}} \\ {1-x} & {,} & {\frac{1}{2} < x \leq 1}\end{array}\right.\) and \(g(x)=\left(x-\frac{1}{2}\right)^{2}, x \in R .\) Then the area (in sq. units) of the region bounded by the curves, \(y=f(x)\) and \(y=g(x)\) between the lines, \(2 \mathrm{x}=1\) and \(2 \mathrm{x}=\sqrt{3},\) isJEE Mains 2020 Hard
More PYQs from JEE Mains
- For \(p\,>\,0\), a vector \(\vec{v}_{2}=2 \hat{i}+(p+1) \hat{j}\) is obtained by rotating the vector \(\vec{v}_{1}=\sqrt{3} p \hat{i}+\hat{j}\) by an angle \(\theta\) about origin in counter clockwise direction. If \(\tan \theta=\frac{(\alpha \sqrt{3}-2)}{4 \sqrt{3}+3}\), then the value of \(\alpha\) is equal to \(....\)JEE Mains 2021 Hard
- Let \(S_n\) denote the sum of first \(n\) terms an arithmetic progression. If \(S_{20}=790\) and \(S_{10}=145\), then \(S_{15}-\) \(S_5\) is :JEE Mains 2024 Medium
- Two tangents are drawn from the point \(\mathrm{P}(-1,1)\) to the circle \(\mathrm{x}^{2}+\mathrm{y}^{2}-2 \mathrm{x}-6 \mathrm{y}+6=0\). If these tangents touch the circle at points \(A\) and \(B\), and if \(D\) is a point on the circle such that length of the segments \(A B\) and \(A D\) are equal, then the area of the triangle \(A B D\) is eqaul to:JEE Mains 2021 Medium
- If in a triangle \(\mathrm{ABC}, \mathrm{AB}=5\) units, \(\angle \mathrm{B}=\cos ^{-1}\left(\frac{3}{5}\right)\) and radius of circum circle of \(\triangle \mathrm{ABC}\) is \(5\) units, then the area (in sq. units) of \(\triangle \mathrm{ABC}\) is:JEE Mains 2021 Hard
- The coefficient of \(x^{7}\) in the expression \((1+x)^{10}+x(1+x)^{9}+x^{2}(1+x)^{8}+\ldots+x^{10}\) isJEE Mains 2020 Hard
- The domain of the function \(\operatorname{cosec}^{-1}\left(\frac{1+\mathrm{x}}{\mathrm{x}}\right)\) is :JEE Mains 2021 Medium