3.7-bo'lim : Teskari trig funksiyalarining hosilalari
5. \(\displaystyle h\left( x \right) = \frac{{{{\sin }^{ - 1}}\left( x \right)}}{{1 + x}}\) ni farqlang.
Yechim
Bu erda sinfdagi formulalar yordamida hosila olishdan boshqa narsa qilish kerak emas.
\[\require{bbox} \bbox[2pt,border:1px solid black]{{h'\left( x \right) = \frac{{\frac{{1 + x}}{{\sqrt {1 - {x^2}} }} - {{\sin }^{ - 1}}\left( x \right)}}{{{{\left( {1 + x} \right)}^2}}} = \frac{{1 + x - \sqrt {1 - {x^2}} {{\sin }^{ - 1}}\left( x \right)}}{{\sqrt {1 - {x^2}} {{\left( {1 + x} \right)}^2}}}}}\]