If `y=x^(tanx)+sqrt((x^2+1)/2)`,find`(dy)/(dx)`

Explanation

`y=x^{tan x}+frac{x^{2}+1}{2}`

`
y=e^{tan x log x}+e^{frac{1}{2} log frac{x^{2}+1}{2}}`

`
frac{d y}{d x}=e^{tan x log x} frac{d}{d x}(tan x log x)+e^{frac{1}{2} log frac{x^{2}+1}{2}} frac{d}{d x}(frac{1}{2} log frac{x^{2}+1}{2})`

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

`
frac{d y}{d x}=x^{tan x}[frac{tan x}{x}+sec ^{2} log x]+sqrt{frac{x^{2}+1}{2}}(frac{x}{x^{2}+1})`

`
frac{d y}{d x}=x^{tan x}[frac{tan x}{x}+sec ^{2} log x]+frac{x}{sqrt{2(x^{2}+1)}} `

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