# Update the Gradient

Apply what we have learned about sigmoids by updating the loss function.

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## Updating the loss function

Now that we have a brand-new loss function, let’s look up its gradient. Here is the partial derivative of the log loss with respect to the weight from the math textbooks:

$\frac{\delta L}{\delta w} = \frac{1}{m} \sum_{i=1}^{m} x_i (\hat{y_i} - y_i)$

This gradient might look familiar. In fact, it closely resembles the gradient of the mean squared error that we have used so far:

$\frac{\delta MSE}{\delta w} = \frac{2}{m}\sum_{i=1}^{m}x(\hat{y_i}-y_i)$

See how similar they are? This means that we can take our previous `gradient()`

function:

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