If $f\left(x\right)=x\left|x\right|$, then its derivative is

Important Questions on Differentiation

EASY

RRC Group D CBT

IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 19 - Differentiation>Exercise 1>Q 169

If $y=x^{\frac{1}{x}}$ then $\frac{dy}{dx}$ vanishes when

EASY

RRC Group D CBT

IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 19 - Differentiation>Exercise 1>Q 170

If $y=2\log \sqrt{x+\sqrt{x^2+9}}$ then $\frac{dy}{dx}=$

EASY

RRC Group D CBT

IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 19 - Differentiation>Exercise 1>Q 171

If $f\left(x\right)={\cos }^{-1}\left[\frac{1}{\sqrt{13}}(2\cos x-3\sin x)\right]$ then $f^{\text{'}}(0.5)=$

EASY

RRC Group D CBT

IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 19 - Differentiation>Exercise 1>Q 172

If $x=t^2$ and $y=t^3$ then $\frac{d^{2}y}{d{x}^2}=$

EASY

RRC Group D CBT

IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 19 - Differentiation>Exercise 1>Q 173

If $y=\cos \left(3{\cos }^{-1}x\right)+\cos \left(2{\cos }^{-1}x\right)\frac{dy}{dx}=$

EASY

RRC Group D CBT

IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 19 - Differentiation>Exercise 1>Q 174

If $y={\sin }^{-1}\left[\sqrt{1-x^2}\tan \left({\sin }^{-1}x\right)\right]$ then $\frac{dy}{dx}=$

HARD

RRC Group D CBT

IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 19 - Differentiation>Exercise 1>Q 175

If $y=\sqrt{\sin x +\sqrt{\sin x +\sqrt{\sin x+\sqrt{\dots .\infty }}}}$  then $\frac{ dy}{dx},y\ne 0$

EASY

RRC Group D CBT

IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 19 - Differentiation>Exercise 1>Q 176

If $x+y={\tan }^{-1}y$ and $\frac{d^{2}y}{d{x}^2}=f\left(y\right)\frac{dy}{dx}$ then $f\left(y\right)=$