How do you differentiate #x/ sqrt (x^2 +1)#?

1 Answer

Answer:

#\frac{1}{(x^2+1)^{3/2}}#

Explanation:

Differentiating given function: #x/\sqrt{x^2+1}# w.r.t. #x# by using quotient rule as follows

#d/dx(x\/sqrt{x^2+1})#

#=\frac{\sqrt{x^2+1}d/dx(x)-xd/dx\sqrt{x^2+1}}{(\sqrt{x^2+1})^2}#

#=\frac{\sqrt{x^2+1}(1)-x\frac{2x}{2\sqrt{x^2+1}}}{(\sqrt{x^2+1})^2}#

#=\frac{x^2+1-x^2}{\sqrt{x^2+1}(x^2+1)}#

#=\frac{1}{(x^2+1)^{3/2}}#