what does d/dx mean? (yes just a d on top and dx on the bottom)
thanks!
thanks!
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Only if y = f(x). If y = g(x), then dy/dx = g'(x).
I know this might be trivially confusing, but it's true. In most cases, y = f(x), anyway, so dy/dx = f'(x)
d/dx means the derivative of something with respect to x. If dy/dx, then it's derivative of y with respect to x, which is also f'(x) if y = f(x).
The reason why this is important is because the definition of the derivative deals with functions:
dy/dx = lim h->0 [f(x + h) - f(x)]/h
What if you are given something where y is not necessarily a function of x? Like
x = y^2 ? This is actually 2 functions in one, y = sqrt(x) and y = -sqrt(x). To find dy/dx, you would have to assume that y is a function of x, and you would use what is called implicit differentiation.
Differentiating both sides of x = y^2, and keeping in mind that y=f(x) you get:
1 = 2y(dy/dx)
dy/dx = 1/(2y)
dy/dx will then depend on whether y = sqrt(x) or y = - sqrt(x)
I know this might be trivially confusing, but it's true. In most cases, y = f(x), anyway, so dy/dx = f'(x)
d/dx means the derivative of something with respect to x. If dy/dx, then it's derivative of y with respect to x, which is also f'(x) if y = f(x).
The reason why this is important is because the definition of the derivative deals with functions:
dy/dx = lim h->0 [f(x + h) - f(x)]/h
What if you are given something where y is not necessarily a function of x? Like
x = y^2 ? This is actually 2 functions in one, y = sqrt(x) and y = -sqrt(x). To find dy/dx, you would have to assume that y is a function of x, and you would use what is called implicit differentiation.
Differentiating both sides of x = y^2, and keeping in mind that y=f(x) you get:
1 = 2y(dy/dx)
dy/dx = 1/(2y)
dy/dx will then depend on whether y = sqrt(x) or y = - sqrt(x)
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Yes. dy/dx is Leibniz notation. f'(x) is Lagrange notation. See links below.
d/dx is a DIFFERENTIAL OPERATOR (see 3rd link below). d/dx in front of anything means find the derivative of that thing with respect to x. Another equivalent operator is Dx, used less frequently.
d/dx is a DIFFERENTIAL OPERATOR (see 3rd link below). d/dx in front of anything means find the derivative of that thing with respect to x. Another equivalent operator is Dx, used less frequently.