Найти производные функций: 1) y=(2x-7)/(3x+5) 2) y=2cos7x

Question

Найти производные функций:

1) y=(2x-7)/(3x+5)

2) y=2cos7x

Answer 1

1) (U/V)' = U'V-UV'/V^2
y=(2x-7)/(3x+5)
y'=((2x-7)/(3x+5))' = 2×(3x+5)-(2x-7)×3/(3x+5)^2=
2×(3x+5)-3×(2x-7)/(3x+5)^2 = 6x+10-6x+21/(3x+5)^2 = 31/(3x+5)^2

2) y=2cos7x
y' = (2cos7x)' = -14sin7x

Answer 2

1) (U/V)' = U'V-UV'/V^2
y=(2x-7)/(3x+5)
y'=((2x-7)/(3x+5))' = 2×(3x+5)-(2x-7)×3/(3x+5)^2=
2×(3x+5)-3×(2x-7)/(3x+5)^2 = 6x+10-6x+21/(3x+5)^2 = 31/(3x+5)^2
2) y=2cos7x
y' = (2cos7x)' = -14sin7x