Question

Differentiate the following w.r.t.x. :

y = `"e"^xsecx - x^(5/3) log x`

Answer 1

Let y = `"e"^xsecx - x^(5/3) log x`

∴ `("d"y)/("d"x) = "d"/("d"x)["e"^x sec x - x^(5/3) log x]`

= `"d"/("d"x)["e"^x sec x] - "d"/("d"x)[x^(5/3) log x]`

= `"e"^x "d"/("d"x) (sec x) + sec x "d"/("d"x) ("e"^x) - [x^(5/3) "d"/("d"x) (log x) + (log x) "d"/("d"x) (x^(5/3))]`

= `"e"^x (sec x tan x) + sec x("e"^x) - x^(5/3) (1/x) - (log x) (5/3 x^(2/3))`

= `"e"^x sec x (tan x + 1) - x^(2/3) (1 + 5/3 log x)`