Question

знайдіть похідну функції

Answer 1

$f(x) = \frac{1}{6} {x}^{6} + 2 {x}^{3} + 4 \sqrt{x} \\ f'(x) = ( \frac{1}{6} {x}^{6} + 2 {x}^{3} + {4}x^{ \frac{1}{2} } ) ' = ( \frac{1}{6} {x}^{6} )' + \\ + (2 {x}^{3} )' + (4 {x}^{ \frac{1}{2} } )' = {x}^{5} + 6 {x}^{2} + 4 \times \frac{1}{2} \times {x}^{ - \frac{1}{2} } = \\ = {x}^{5} + \frac{2}{ \sqrt{x} } + 6 {x}^{2}$