Advertisements
Advertisements
Question
The derivative of \[\sec^{- 1} \left( \frac{1}{2 x^2 + 1} \right) \text { w . r . t }. \sqrt{1 + 3 x} \text { at } x = - 1/3\]
Options
does not exist
0
1/2
1/3
Solution
does not exist
\[\text { We know that } \sec^{- 1} \alpha\text { is not defined for }\alpha \in \left( - 1, 1 \right)\]
\[\text { Here for } x = \frac{- 1}{3}, \frac{1}{2 x^2 + 1} = \frac{9}{11} \in \left( - 1, 1 \right)\]
\[ \therefore \sec^{- 1} \left( \frac{1}{2 x^2 + 1} \right)\text { is not defined at } x = \frac{- 1}{3}\]
\[ \therefore \text { Derivative of } \sec^{- 1} \left( \frac{1}{2 x^2 + 1} \right) \text { does not exist at } x = \frac{- 1}{3}\]
APPEARS IN
RELATED QUESTIONS
Differentiate tan (x° + 45°) ?
Differentiate `2^(x^3)` ?
Differentiate \[3^{e^x}\] ?
Differentiate \[e^x \log \sin 2x\] ?
Differentiate \[\frac{x^2 + 2}{\sqrt{\cos x}}\] ?
Differentiate \[\cos \left( \log x \right)^2\] ?
Differentiate \[\tan^{- 1} \left\{ \frac{x}{\sqrt{a^2 - x^2}} \right\}, - a < x < a\] ?
Differentiate \[\tan^{- 1} \left\{ \frac{x}{1 + \sqrt{1 - x^2}} \right\}, - 1 < x < 1\] ?
Differentiate \[\tan^{- 1} \left( \frac{\sqrt{x} + \sqrt{a}}{1 - \sqrt{xa}} \right)\] ?
Differentiate
\[\tan^{- 1} \left( \frac{\cos x + \sin x}{\cos x - \sin x} \right), \frac{\pi}{4} < x < \frac{\pi}{4}\] ?
If \[y = \sin^{- 1} \left( \frac{2x}{1 + x^2} \right) + \sec^{- 1} \left( \frac{1 + x^2}{1 - x^2} \right), 0 < x < 1,\] prove that \[\frac{dy}{dx} = \frac{4}{1 + x^2}\] ?
If \[y = \sin^{- 1} \left( 6x\sqrt{1 - 9 x^2} \right), - \frac{1}{3\sqrt{2}} < x < \frac{1}{3\sqrt{2}}\] \[\frac{dy}{dx} \] ?
Find \[\frac{dy}{dx}\] in the following case \[4x + 3y = \log \left( 4x - 3y \right)\] ?
Find \[\frac{dy}{dx}\] in the following case \[\sin xy + \cos \left( x + y \right) = 1\] ?
If \[\sec \left( \frac{x + y}{x - y} \right) = a\] Prove that \[\frac{dy}{dx} = \frac{y}{x}\] ?
Differentiate \[x^{1/x}\] with respect to x.
Differentiate \[\left( \log x \right)^{\cos x}\] ?
Differentiate \[x^{\sin^{- 1} x}\] ?
Differentiate \[\left( \cos x \right)^x + \left( \sin x \right)^{1/x}\] ?
Find \[\frac{dy}{dx}\] \[y = x^{\log x }+ \left( \log x \right)^x\] ?
\[\text { If }x = \cos t\left( 3 - 2 \cos^2 t \right), y = \sin t\left( 3 - 2 \sin^2 t \right) \text { find the value of } \frac{dy}{dx}\text{ at }t = \frac{\pi}{4}\] ?
Differentiate \[\sin^{- 1} \left( 2x \sqrt{1 - x^2} \right)\] with respect to \[\tan^{- 1} \left( \frac{x}{\sqrt{1 - x^2}} \right), \text { if }- \frac{1}{\sqrt{2}} < x < \frac{1}{\sqrt{2}}\] ?
If f (x) = loge (loge x), then write the value of `f' (e)` ?
If \[f\left( 0 \right) = f\left( 1 \right) = 0, f'\left( 1 \right) = 2 \text { and y } = f \left( e^x \right) e^{f \left( x \right)}\] write the value of \[\frac{dy}{dx} \text{ at x } = 0\] ?
If \[y = x^x , \text{ find } \frac{dy}{dx} \text{ at } x = e\] ?
If \[y = \log \sqrt{\tan x}, \text{ write } \frac{dy}{dx} \] ?
If \[y = \log \left| 3x \right|, x \neq 0, \text{ find } \frac{dy}{dx} \] ?
Differential coefficient of sec(tan−1 x) is ______.
If \[\sin y = x \cos \left( a + y \right), \text { then } \frac{dy}{dx}\] is equal to ______________ .
Find the second order derivatives of the following function x3 + tan x ?
If y = e−x cos x, show that \[\frac{d^2 y}{d x^2} = 2 e^{- x} \sin x\] ?
If y = x3 log x, prove that \[\frac{d^4 y}{d x^4} = \frac{6}{x}\] ?
If x = a cos θ, y = b sin θ, show that \[\frac{d^2 y}{d x^2} = - \frac{b^4}{a^2 y^3}\] ?
If y = a xn + 1 + bx−n and \[x^2 \frac{d^2 y}{d x^2} = \lambda y\] then write the value of λ ?
If x = t2 and y = t3, find \[\frac{d^2 y}{d x^2}\] ?
If \[y = \log_e \left( \frac{x}{a + bx} \right)^x\] then x3 y2 =
Differentiate sin(log sin x) ?
