Tolong dong yang ngerti

Tolong dong yang ngerti

Jawaban Terkonfirmasi

Jika tidak terlihat lihat lampiran

$displaystyle text{Misalkan:}\\u=frac{xsqrt3}{1-x^2}\\frac{du}{dx}=frac{sqrt{3}(1-x^2)+2x(xsqrt{3})}{(1-x^2)^2}\\~~~~~=frac{sqrt{3}-x^2sqrt3+2x^2sqrt{3}}{(1-x^2)^2}\\~~~~~=frac{sqrt{3}(1+x^2)}{(1-x^2)^2}\\y=frac{1}{sqrt3} arc tan u\\frac{dy}{du}=frac{1}{sqrt3(u^2+1)}=frac{1}{sqrt3((frac{xsqrt3}{1-x^2})^2+1)}=frac{(1-x^2)^2}{sqrt3(3x^2+(1-x^2)^2})\$

$displaystyle text{Sehingga:}\\frac{dy}{dx}=frac{dy}{du}.frac{du}{dx}\\~~~~~=frac{sqrt{3}(1+x^2)}{(1-x^2)^2}timesfrac{(1-x^2)^2}{sqrt3(3x^2+(1-x^2)^2)}\\~~~~=frac{x^2+1}{3x^2+x^4-2x^2+1}\\~~~~=frac{x^2+1}{x^4+x^2+1}$

Gambar Jawaban