Find the derivative of the function y=x² /arctgx ?
1 Answer
Jun 14, 2018
Explanation:
y=x^2/arctanxy=x2arctanx
y=x^2(arctanx)^-1y=x2(arctanx)−1
Let's differentiate this using the product rule.
dy/dx=(d/dxx^2)(arctanx)^-1+x^2(d/dx(arctanx)^-1)dydx=(ddxx2)(arctanx)−1+x2(ddx(arctanx)−1)
The derivative of
dy/dx=2x(arctanx)^-1+x^2(-(arctanx)^-2)(d/dxarctanx)dydx=2x(arctanx)−1+x2(−(arctanx)−2)(ddxarctanx)
dy/dx=2x(arctanx)^-1-x^2(arctanx)^-2(1/(x^2+1))dydx=2x(arctanx)−1−x2(arctanx)−2(1x2+1)
dy/dx=(arctanx)^-2(2xarctanx-x^2/(x^2+1))dydx=(arctanx)−2(2xarctanx−x2x2+1)