The total derivative of the function z=f(x,y) with respect to x is:(adsbygoogle = window.adsbygoogle || []).push({});

dz/dx = ∂z/∂x + (∂z/∂y)(dy/dx)

The way i see this is that the total derivative, dz/dx, gives the rate of change of z with x, allowing y to vary with x at the rate dy/dx. I don't know if this is right.

The directional derivative Daf(x,y) gives the rate of change of z in the direction of the vector a^{→}. But, im thinking, that for a particular direction, there is a line: y=mx +b, and y is a function of x. A certain direction gives a unique dy / dx. If i substitute this in the equation for a total derivative, I get a unique dz/dx.

My question is, what really is a total derivative?

I'm asking this since the way i understand it seems to blur the difference between directional and total derivatives. PLease help. Thanks in advance!!

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# Total and directional derivatives:

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