Question

Найти производную функции
1)$f(x)= sqrt{1-3 x^{2} } + frac{1}{ x^{2}+4 }$
2)$f(x)=(8-3 x^{6} )^{3}- frac{ x^{2} }{5- x^{2} }$

Answer 1

$2)f`(x)=3cdot(8-3 x^{6}) ^{2} cdot(8-3 x^{6})`- frac{( x^{2})`(5- x^{2} )- x^{2} (5- x^{2} )` }{(5- x^{2} ) ^{2} } = \ =3 cdot(8-3 x^{6}) ^{2}cdot (-18x^{5}) - frac{ 2x(5- x^{2} )- x^{2} (-2 x ) }{(5- x^{2} ) ^{2} } = \ =-54x^{5} cdot(8-3 x^{6}) ^{2} - frac{ 10x-2 x^{3} +2 x^{3} }{(5- x^{2} ) ^{2} } = \= -54x^{5} cdot(8-3 x^{6}) ^{2} - frac{ 10x }{(5- x^{2} ) ^{2} }$$1)f`(x)= frac{1}{2 sqrt{1-3 x^{2} } } cdot(1-3 x^{2} )`- frac{1}{( x^{2} +4) ^{2} } cdot( x^{2} +4)`= \ =frac{-6x}{2 sqrt{1-3 x^{2} } }- frac{2x}{( x^{2} +4) ^{2} }=frac{-3x}{sqrt{1-3 x^{2} } }- frac{2x}{( x^{2} +4) ^{2} }$