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Gradient Descent - Problem of Hiking Down a MountainUdacityHave you ever climbed a mountain? I am sure you had to hike down at some point? Hikingdown is a great exercise and it is going to help us understand gradient descent.Whats the goal when you are hiking down a mountain?- To have fun and toreach the bottom. Let’s focus on reaching the bottom for now.What is the red dot doing when it’s hiking down?It’s always going in the downwarddirection, until it hits the bottom. Let’s call our friend calculus and see what she has tosay about this.DerivativesBefore we hop in, let me remind you a little bit about derivatives. There are different waysto look at derivatives, two of the most common ones are•Slope of the tangent line to the graph of the function•Rate of change of the function1
Following are some of the common derivatives:•d(x2)dx= 2x•d(-2y5)dy=-10y4•d(5-θ)2dθ=-2(5-θ) (negative sign coming from-θ)Sounds great! What if, we have more than one variable in our function? Well, we will talkabout partial derivatives then! Let’s look at some examples:•∂∂x(x2y2) = 2xy2•∂∂y(-2y5+z2) =-10y4•∂∂θ2(5θ1+ 2θ2-12θ3) = 2•∂∂θ2(0.55-(5θ1+ 2θ2-12θ3)) =-2 (Can you convince yourself where the-is comingfrom?)