Embibe Experts Solutions for Chapter: Differential Coefficient, Exercise 1: Assam CEE 2016

If $f^{\text{'}}\left(\sqrt{3}\right)=\sqrt{3}, g^{\text{'}}\left(2\right)=\sqrt{2}$; then the derivative of $f\left(\cot x\right)$ with respect to $g\left(\csc x\right)$ at $x=\frac{\pi }{6}$ is

If $y$ is a function of $x$ and $\log \left(x+y\right)=2xy$ then the value of $y^{\text{'}}\left(0\right)$ is equal to

Let $f^{\text{'}\text{'}}\left(x\right)=-f\left(x\right)$, where $f$ is continuous double differentiable function and $g\left(x\right)=f^{\text{'}}\left(x\right)$. If $F\left(x\right)={\left(f\left(\frac{x}{2}\right)\right)}^2+{\left(g\left(\frac{x}{2}\right)\right)}^2$ and $F\left(5\right)=5$, then $F\left(10\right)$ is

Let $f$ be a real-valued function defined on $\left(0,1\right)\cup \left(2,4\right)$, such that $f^{\text{'}}\left(x\right)=0\forall x$, then