Contrary to popular belief, calculus is not just for math nerds or people who wear pocket protectors. It’s actually pretty cool and can be used in real-life situations like finding the slope of a line (which is basically how much your car will cost you if gas prices go up), or figuring out how fast something is moving (like that time you accidentally spilled coffee on yourself while running to class).

Now, derivatives. A derivative is essentially just finding the slope of a line at any given point. This can be done using calculus, which involves taking limits and doing some fancy math stuff.

First, let’s say you have a function like this: y = x^2 + 3x + 1. To find the derivative of this function (which is essentially finding the slope at any given point), you would take the limit as h approaches zero and divide by h:

f'(x) = lim h->0 [(y+h)-y]/h

This might seem like a lot of work, but trust us it’s worth it. Once you have your derivative, you can use it to find things like the maximum or minimum value of a function (which is basically finding out where the slope changes direction), or to graph functions on a coordinate plane (which is essentially just drawing lines).

Now gradients. A gradient is essentially just finding the steepest part of a line at any given point. This can be done using calculus, which involves taking limits and doing some fancy math stuff.

First, let’s say you have a function like this: z = x^2 + y^2. To find the gradient of this function (which is essentially finding out where the slope changes direction), you would take partial derivatives with respect to both x and y:

z/x = 2x
z/y = 2y

This might seem like a lot of work, but trust us it’s worth it. Once you have your gradient, you can use it to find things like the direction in which a function is increasing or decreasing (which is basically finding out where the slope changes direction), or to graph functions on a coordinate plane (which is essentially just drawing lines).