Question

Найти производную y=(x+5)^2 * arccos^3 (5x)

Answer 1

Ответ:

$y' = 2 (x + 5) \times {arccos}^{3} (5x) + 3 {arccos}^{2} (5x) \times ( - \frac{1}{ \sqrt{1 - 25 {x}^{2} } } ) \times 5 \times {(x + 5)}^{2} = \\ 2(x + 5) {arccos}^{3} (5x) - \frac{5 {arccos}^{2}(5x) {(x + 5)}^{2} }{ \sqrt{1 - 25 {x}^{2} } } = \\ (x + 5) {arccos}^{2} (5x)(2arccos(5x) - \frac{5(x + 5)}{ \sqrt{1 - 25 {x}^{2} } } )$