Solve any maths problem

Step by step

1. \frac{d}{dy}\left[x^{2} y + y^{3}\right]

   Differentiate 2 times, one derivative at a time.

2. \frac{d}{d y} y^{3} + \frac{\partial}{\partial y} x^{2} y

   Sum rule: differentiate term by term.

3. 3 y^{2} + \frac{\partial}{\partial y} x^{2} y

   Power rule: (xⁿ)′ = n·xⁿ⁻¹ with n = 3.

4. x^{2} \frac{d}{d y} y + 3 y^{2}

   Constant multiple rule: pull the constant out.

5. x^{2} + 3 y^{2}

   d/dx of x is 1.

6. f^{(1)}(y) = x^{2} + 3 y^{2}

   That is derivative number 1.

7. \frac{d}{d y} x^{2} + \frac{d}{d y} 3 y^{2}

   Sum rule: differentiate term by term.

8. \frac{d}{d y} 3 y^{2}

   The derivative of a constant is 0.

9. 3 \frac{d}{d y} y^{2}

   Constant multiple rule: pull the constant out.

10. 6 y

    Power rule: (xⁿ)′ = n·xⁿ⁻¹ with n = 2.

11. f^{(2)}(y) = 6 y

    That is derivative number 2.

Reveal the answer

f''(y) = 6 y