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My teacher taught us what is the gradient of a function and what it means. But in this equation: df = ∇f dl , I dont know how to solve ∇f. My teacher put this

Can anyone please teach me how to solve step by step that equation? I tried but I dont get to the same result. Thanks in advance!

victor26567
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You don’t have to solve anything it’s simply the differential of $f$expressed by a dot product of the gradient and $d\vec l$, thus

$$df =\nabla f \cdot d\vec l=f_x dx+f_ydy+f_zdz$$

user
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  • No, I mean, imagine you want to calculate the gradient operator in different systems (cartesian,cylindrical,spherical). And let's say that "df" and "dl" are known values and you have to solve "∇f" for seeing what its look like in different coordinates systems. How can you solve that gradient? – victor26567 Feb 10 '18 at 15:12
  • Solve a system of d linear equations corresponding to different directional derivatives, where d is the dimension. Just one DF and do will not be enough except in one dimension. – Ian Feb 10 '18 at 15:26
  • @user71209 You can obtain the expression for other coordinates system by chain rule, see this example here https://math.stackexchange.com/questions/1971674/missing-1-r-factor-in-gradient-of-polar-function – user Feb 10 '18 at 15:28
  • I see it much harder that it really is. There is not another simple way to solve it? I mean like a equation, nor matrix nor chain rule – victor26567 Feb 10 '18 at 15:31
  • @user71209 I don't know any shortcut for it – user Feb 10 '18 at 15:31