Question

Решить дифференциал прозводных

Answer 1

$1){y}^{.} = 10 {x}^{4} - 18 {x}^{2} + 14x - 8 \\ \\ {y}^{.} ( - 2) = 10( { - 2})^{4} - 18 {( - 2)}^{2} + 14( - 2) - 8 = 160 - 72 - 28 - 8 = 52$

$2) {y}^{.} = (6 {x}^{2} - 4 {x}^{3} )( {x}^{6} + {x}^{5} ) + (2 {x}^{3} - {x}^{4} )(6 {x}^{5} + 5 {x}^{4} ) \\ \\ {y}^{.} (1) = (6 - 4)(1 + 1) + (2 - 1)(6 + 5) = 4 + 11 = 15$

$3){y}^{.} = \frac{ - 21 {x}^{2} + 5 }{3x + 8} - \frac{3(5x - 7 {x}^{3} )}{ ({3x + 8)}^{2} } \\ \\ {y}^{.} ( - 1) = \frac{ - 21 + 5}{ - 3 + 8} - \frac{3( - 5 + 7)}{ {( - 3 + 8)}^{2} } = \frac{ - 16}{5} - \frac{6}{25} = - \frac{86}{25} = - 3 \frac{11}{25}$