Question

Differentiate the given expression with respect to x. (show steps) ​

Answer 1

answer = -40x/(x^2-4)^2

Answer 2

$\rightarrow V=\frac{20}{x^2-4}\\\\\\\text{Differentiating above equation wrt x on both sides, we get:}\\\\\\\rightarrow \frac{dV}{dx}= \frac{d}{dx}[\frac{20}{x^2-4}]\\\\\\\text{Now,as 20 is constant we will take it out. }\\\\\\\text{Also, \frac{1}{x^2-4} can be written as (x^2-4)^{-1} .}\\\\\\\rightarrow \frac{dV}{dx}= 20 \times \frac{d}{dx}(x^2-4)^{-1}\\\\\\\text{Applying chain rule we get;}\\\\\\\rightarrow \frac{dV}{dx}=20[-1(x^2-4)^{-1-1} \times \frac{d}{dx}(x^2-4)]$

$\rightarrow \frac{dV}{dx}=20[-1(x^2-4)^{-2}\times \frac{d}{dx}(x^2-4)]\\\\\\\rightarrow \frac{dV}{dx}=20[-1(x^2-4)^{-2} \times (2x^{2-1}-0)]\\\\\\\rightarrow \frac{dV}{dx}=20[-1(x^2-4)^{-2} \times (2x)]\\\\\\\rightarrow \frac{dV}{dx}=-20[\frac{2x}{(x^2-4)^{2}}]\\\\\\\rightarrow \frac{dV}{dx}=\frac{-40x}{(x^2-4)^{2}}$

Note : You can solve it further to simplify the equation .