They both mean the derivative of the function y right? So do they mean the same thing and they're just different notations, or do they actually mean different things?
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Whenever you are only differentiating with respect to one variable, like x or t, then it doesn't matter. y' or f'(x) is just a shorthand. If you are doing multi-variable calculus, you may have a dy/dx and a dy/dz in the same equation. Then you need to use the longer form.
I prefer dy/dx because it helps you remember what calculus really means. The derivative is the limit of rise over run as the interval on which you're measuring gets infinitely small. Rise over run is just the slope, which is why the derivative gives you the slope.
It also helps with integrals. ydx gives you rise times run, which is the area under the curve. That's why area under the curve is the opposite of slope. (dy/dx)dx=dy, which is the change in the hight of y. When doing an integral, that's what you find out, then you need to add a constant to get y=(dy/dx)dx+c.
(that's missing a bit of notation and glosses over some details of the explanation, but it gets you into the right frame of mind for understanding calculus).
I prefer dy/dx because it helps you remember what calculus really means. The derivative is the limit of rise over run as the interval on which you're measuring gets infinitely small. Rise over run is just the slope, which is why the derivative gives you the slope.
It also helps with integrals. ydx gives you rise times run, which is the area under the curve. That's why area under the curve is the opposite of slope. (dy/dx)dx=dy, which is the change in the hight of y. When doing an integral, that's what you find out, then you need to add a constant to get y=(dy/dx)dx+c.
(that's missing a bit of notation and glosses over some details of the explanation, but it gets you into the right frame of mind for understanding calculus).
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They both mean the same thing. The rate at which y changes related to x. However, it is better to get used to using dy/dx, because later in calculus you use variations of it (dx/dt, dy/dt, dtheta/dr, etc.). Also, there are problems where you may need to anti-derive both an x-quantity and a y-quantity, and in that case it is good to know that dy/dx is a fraction that can be broken up.
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Its really the same thing, I prefer y' because its easier to write
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f '(x) or y' or dy/dx
will all do for the derivative...sometimes one way is more convenient to use in a problem...
when you are doing implicit differentiation, y' can be more convenient notation...
don't get upset !
will all do for the derivative...sometimes one way is more convenient to use in a problem...
when you are doing implicit differentiation, y' can be more convenient notation...
don't get upset !
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You can use either one whenever you want really, but dy/dx is easier to work with for things like integration and related rates. I would only use y' for when I'm just taking a simple derivative.