Question

нахождение значения производной в точке. 1) y=7x+4. 2)y=3x^2-x. 3)y=ln(5x+1). 4)y=sin2x. 5)y=(x-3)^2. 6)y=x^3. 7)y=e^3x

Answer 1

1) y'=(7x+4)' = 7

2) y' = (3x²-x)' = 6x-1

3) y'=(ln(5x+1))' = (1/(5х+1) ) * (5х+1)' = (1/(5х+1) ) * 5 = 5/(5х+1)

4) y' = (sin2x)' = cos2x * (2x)' = 2cos2x

5) y' = ((x-3)²)' = (x²-6x+9)' = 2x-6

6) y' = (x³)' = 3x²

7) y' = e^3x = e^3x * (3x)' = 3e^3x