# Week 2: Optimization with gradients

Hi, in the video Partial derivatives - Part 1, we’re shown the following:

Then we’re asked to solve the extension of this principal in “Optimization with gradients: An example.”

If I “treat y as a constant” as instructed earlier then every term with a y will become zero because the derivative of a constant is 0. The result is 85-0 = 85. However, correct answer is provided as:

The correct logic must be different than what we are shown in the early example because it does not provide the correct solution when applied here. Can you please provide the step-by-step solution?

Thank you

This link solved my issue. Thanks

I’m glad you found an explanation.

That’s only true if the constant is not a function of the derivative term.
For example the derivative/dx of 5x is 5, not 0.
The partial derivative /dx of 5xy would be 5y.

But the derivative of 5 (without the ‘x’ or ‘y’ terms) would be 0.

Nope, only if its and additive standalone term it will be zero.