Question

Найти дифференциал функции
y=x-3/x
y=(x-5)(x+2)
y=e^-x
y=sin5x
y=ln cos x

Answer 1

$1)y = x - \frac{3}{x} = x - 3 {x}^{ - 1} \\$

$y' = 1 + 3 {x}^{ - 2} = 1 + \frac{3}{ {x}^{2} } \\$

$dy = (1 + \frac{3}{ {x}^{2} } )dx \\$

$2)y = (x - 5)(x + 2) = {x}^{2} - 5x + 2x - 10 = \\ = {x}^{2} - 3x - 10$

$y '= 2x - 3 \\ dy = (2x - 3)dx$

$3)y = {e}^{ - x}$

$y '= - {e}^{ - x} \\ dy = - {e}^{ - x} dx$

$4)y = \sin(5x)$

$y' = 5 \cos(5x) \\ dy = 5 \cos(5x) dx$

$5)y = ln( \cos(x) )$

$y '= \frac{1}{ \cos(x) } \times ( - \sin(x)) = - tg(x) \\$

$dy = - tg(x)dx$