What is meaning of dy/dx?

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G Prasad

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If y is a function of x then dy/dx corresponds to the change in y for a small increment in x as that change in x tends to zero.
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GMAT Math Expert

differentiation of y in terms of x
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Tutor

Rate of change of y w.r.to x.
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Super teacher

it means slope of the y when plotted against x.
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Tutor - Maths and computer science

dy/dx show how fast something is changing (called the rate of change) at any point.
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Online Tutor

Remember back to basic Algebra I, when the slope of a line was given by m=?y/?x? And, what is a derivative, but the slope of a (tangent) line? Indeed, if you look back at the limit definition of the derivative, it's really nothing more than the limit of ?y/?x as ?x?0. Thus, you can think of the "d"...
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Remember back to basic Algebra I, when the slope of a line was given by m=?y/?x? And, what is a derivative, but the slope of a (tangent) line? Indeed, if you look back at the limit definition of the derivative, it's really nothing more than the limit of ?y/?x as ?x?0. Thus, you can think of the "d" in "dy" and "dx" as a very tiny delta. (Indeed, Leibniz' notion of the derivative involved infinitessimal ?'s; unfortunately, it would take a couple centuries before a formal notion of "infinitessimal" could be developed to rescue Leibniz!) So, just like in ?y/?x, the "d" means "change." And, just like in ?y/?x, it really doesn't make much sense to talk about ?y without ?x, or vice versa! (That is, they represent a RELATIVE change: the change in y relative to a certain change in x.) However, in differential equations, we can split the dy from the dx on opposite sides of the equality, because we're still maintaining the relationship between dy and dx. For example, if dy/dx = y²sinx, then the equation dy/y² = sinxdx really tells how dy and dx are related to each other! read less
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Home Tutor

dy/dx means differential coefficient of y with respect to x.
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Graduate

differentiating y with respect to x
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Physics Guru

meaning of dy/dx change in y with respect to change in x directions The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function or dependent variable) which is determined by another quantity (the independent variable).
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