Question

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

y = (x³ – 2) tan x – x cos x + 7^x. x⁷

Answer 1

Let y = (x³ – 2) tan x – x cos x + 7^x. x⁷  

∴ `("d"y)/("d"x) = "d"/("d"x) [(x^3 - 2) tan x - x cos x + 7^x*x^7]`

= `"d"/("d"x)[(x^3 - 2) tan x] - "d"/("d"x)[x cos x] + "d"/("d"x) [7^x*x^7]`

= `(x^3 - 2) "d"/("d"x) (tan x) + (tan x) "d"/("d"x) (x^3 - 2) - [x "d"/("d"x) (cos x) + (cos x) "d"/("d"x) (x)] + 7^x "d"/("d"x) (x^7) + x^7 "d"/("d"x)(7^x)`

= (x³ – 2)(sec²x) + (tan x)(3x² – 0) – [x(– sin x) + (cos x)(1)] + 7^x (7x⁶) + x⁷ (7^x log 7)

= (x³ – 2)sec²x + 3x² tan x + x sin x – cos x + 7^x. x⁶ [7 + x log 7]