a) Write the derivative of sinh x with respect to x. b) Under which necessary condition, \( \frac{d}{dx}(\text{sech}^{-1}x) =…

a) Write the derivative of sinh x with respect to x. 

b) Under which necessary condition, \( \frac{d}{dx}(\text{sech}^{-1}x) = -\frac{1}{x\sqrt{1-x^2}} \) 

c) Write the meaning of dy and \( \Delta y \) in percentage error in the estimate\( = \frac{\Delta y - dy}{y} \times 100\% \)

 d) Write the integral of \( \int \frac{1}{\sqrt{x^2 - a^2}} dx \)

e) Write the integrating factor (I.F.) in a linear differential equation of the form \( \frac{dy}{dx} \) + Py = Q$ where P and Q are functions of x. [1]