Solve any maths problem

Step by step

1. \frac{d}{dy}\left[y \left(1 - y\right)\right]

   Differentiate 2 times, one derivative at a time.

2. y \frac{d}{d y} \left(1 - y\right) + \left(1 - y\right) \frac{d}{d y} y

   Product rule with u = y and v = 1 - y: (uv)′ = u′v + uv′.

3. y \left(\frac{d}{d y} 1 + \frac{d}{d y} \left(- y\right)\right) + \left(1 - y\right) \frac{d}{d y} y

   Sum rule: differentiate term by term.

4. y \frac{d}{d y} \left(- y\right) + \left(1 - y\right) \frac{d}{d y} y

   The derivative of a constant is 0.

5. - y \frac{d}{d y} y + \left(1 - y\right) \frac{d}{d y} y

   Constant multiple rule: pull the constant out.

6. 1 - 2 y

   d/dx of x is 1.

7. f^{(1)}(y) = 1 - 2 y

   That is derivative number 1.

8. \frac{d}{d y} 1 + \frac{d}{d y} \left(- 2 y\right)

   Sum rule: differentiate term by term.

9. \frac{d}{d y} \left(- 2 y\right)

   The derivative of a constant is 0.

10. - 2 \frac{d}{d y} y

    Constant multiple rule: pull the constant out.

11. -2

    d/dx of x is 1.

12. f^{(2)}(y) = -2

    That is derivative number 2.