Question

Найти производную функции 1) 2)

Answer 1

$2)f`(x)=3\cdot(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} }$