Partial Derivative of $L[\phi]$ with respect to $\phi_0$ and $\phi_1$

Question

Problem 2.1 from Simon Prince's "Understanding Deep Learning".

$L[\phi] = \sum_{i=1}^I (\phi_0 + \phi_1x_i - y_i)^2$

Find $\frac{\partial L}{\partial\phi_0}$ and $\frac{\partial L}{\partial\phi_1}$

I have the following:

$\frac{\partial L}{\partial\phi_0} = 2 \sum_{i=1}^I (\phi_0 + \phi_1x_i - y_i)$

$\frac{\partial L}{\partial\phi_1} = 2 \sum_{i=1}^I (\phi_0 + \phi_1x_i - y_i)x_i$

Is this correct? Thank you.

Answer 1

$\frac{\partial L}{\partial\phi_0}$ and $\frac{\partial L}{\partial\phi_1}$ are:

$\frac{\partial L}{\partial\phi_0} = 2 \sum_{i=1}^I (\phi_0 + \phi_1x_i - y_i)$

$\frac{\partial L}{\partial\phi_1} = 2 \sum_{i=1}^I (\phi_0 + \phi_1x_i - y_i)x_i$