Confusion surrounding differentiation of parameter vector ridge regression

Let $$\mathbf{\beta}$$ be the parameter vector of a ridge regression.

Now we can say that:

$$$$\frac{\partial \lambda \beta^T \beta}{\partial \beta}=2\lambda\beta.$$$$

Why is this?

I thought that $$\frac{d}{dx} x^t x = 2x^t$$

Which would imply that:

$$$$\frac{\partial \lambda \beta^T \beta}{\partial \beta}=2\lambda\beta^{T}.$$$$