Differentiate the following functions with respect to `x :` `log(secx+tanx)` (ii) `e^(xsinx)` `sin^(-1)(x^3)` (iv) `sin^(-1)((a+bcosx)/(b+acosx)),b > a`

Explanation

Let `y=log (sec x+tan x)`


we know that `frac{{d}(sec x)}{d x}=sec x tan x, frac{d(tan x)}{d x}=sec ^{2} x, frac{d(log x)}{d x}=frac{1}{x}`



`frac{d y}{d x}=frac{1}{sec x+tan x} times(sec x tan x+sec ^{2} x)`




`frac{d y}{d x}=frac{1}{sec x+tan x} sec x(tan x+sec x)=sec x`