Question

Найдите производную функцию

Answer 1

$(4x + 2 {x}^{4} )' = 4 + 2 \times 4 {x}^{3} = \\ = 4 + 8 {x}^{3}$

$( \sin(x) + {x}^{2} )' = \cos(x) + 2x$

$( \cos(x) - \sqrt{x} )' = - \sin(x) - \frac{1}{2} {x}^{ - \frac{1}{2} } = \\ = - \sin(x) - \frac{1}{2 \sqrt{x} }$

$(6 \sin(x)) = 6 \cos(x)$

$( {x}^{2} \sin(x))' = ( {x}^{2} )' \sin(x) + ( \sin( x))' \times {x}^{2} = \\ = 2x \sin(x) + {x}^{2} \cos(x)$

$( \frac{2x + 5}{3 {x}^{3} } ) '= \frac{(2x + 5) '\times 3 {x}^{3} - (3 {x}^{3} )'(2x + 5) }{9 {x}^{6} } = \\ = \frac{2 \times 3 {x}^{3} - 9 {x}^{2}(2x + 5) }{9 {x}^{6} } = \\ = \frac{6 {x}^{3} - 18 {x}^{3} - 45 {x}^{2} }{9 {x}^{6} } = - \frac{12 {x}^{3} + 45 {x}^{2} }{9 {x}^{6} } = \\ = - \frac{3 {x}^{2}( 4x + 15)}{9 {x}^ {6} } = - \frac{4x + 15}{3 {x}^{4} }$