Differentiate \(\sin^{-1}(\log\tan x)\). Find the \(n\)th differential coefficients of \[ \text{(1) } x^2e^{ax}, \quad \text{(ii) } \frac{1}{1+x^3}. \]
Explain how to find the maxima and minima values of a function of \(x\).
Find the values of \(x\) that give maximum or minimum values to \((x-a)^2(x-b)^3\), distinguishing the cases according as \(a>=
Prove that for a plane curve the radius of curvature \(\rho=r\frac{dr}{dp}\). Shew that the radius of curvature at a point of the curve \(r^n=a^n\cos n\theta\) is \(a^n/\{(n+1)r^{n-1}\}\).