Embibe Experts Solutions for Chapter: Differential Coefficient, Exercise 1: KCET (UG) 2018

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

If $a$ and $b$ are fixed non-zero constants, then the derivative of $\frac{a}{x^4}-\frac{b}{x^2}+\cos x$ is $ma+nb-p$ where

If $y={\left(\cos x^2\right)}^2,$ then $\frac{dy}{dx}$ is equal to

Consider the following statements:
Statement 1: If $y={\log }_{10}x+{\log }_{e}x$, then $\frac{dy}{dx}=\frac{{\log }_{10}e}{x}+\frac{1}{x}$.
Statement 2: $\frac{d}{dx}\left({\log }_{10}x\right)=\frac{\log x}{\log 10}$ and $\frac{d}{dx}\left({\log }_{\mathit{e}}x\right)=\frac{\log x}{\log e}$.

If $y=(x-1{)}^2(x-2{)}^3(x-3{)}^5,$ then $\frac{dy}{dx}$ at $x=4$ is equal to

A particle starts from rest and its angular displacement (in radians) is given by $\theta =\frac{t^2}{20}+\frac{t}{5}.$ If the angular velocity at the end of $t=4$ is $k,$ then the value of $5k$ is

For constant $a$, $\frac{d}{dx}\left(x^x+x^a+a^x+a^a\right)$ is

If the parametric equation of curve is given by $x=\cos \theta +\mathrm{logtan}\frac{\theta }{2}$ and $y=\sin \theta ,$ then the points for which $\frac{dy}{dx}=0$ are given by