1.

Find the derivative of the following functions (it is to be understand that a,b,c,d,p,q,r and s are fixed non-zero constants and m and n are integers): `(x+cos x)(x-tan x)`

Answer» Let `y=(x+cos x)(x-tan x)`
`rArr(dy)/(dx)=(d)/(dx)[(x+cos x)(x-tan x)`
`+(x-tan x)(d)/(dx)(x+cos x)`
`=(x+cos x)(1-sec^(2)x)+(x-tanx)(1-sinx)`
`=-(x+cos x) tan ^(2)x`
`+(x-tan x)(1-sinx)`


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