Differentiate the following functions with respect to `x`
`log(x+sqrt(x^2+1))`

Explanation

Let `y=(x+sqrt{x^{2}+1})`


On differentiating y with respect to `x`, we get


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


We know `frac{d}{d x}(log x)=frac{1}{x}`


`Rightarrow frac{d y}{d x}=frac{1}{x+sqrt{x^{2}+1}} frac{d}{d x}(x+sqrt{x^{2}+1})`


[using chain rule]



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


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