His point is that you can actually solve for L in this one and find the derivative as an explicit function, involving only K. But cubing both sides is also an easier way to get the implicit derivative:
Originally posted by CZeke His point is that you can actually solve for L in this one and find the derivative as an explicit function, involving only K. But cubing both sides is also an easier way to get the implicit derivative:
Originally posted by sonhouse For us not so brilliant in math, what is the differance between implicit and explicit functions?
A function is a function, whatever the situation.
Whether it's 'explicit' or 'implicit' is to do with how it's written down.
F(x) = 2x+9
G(x)^5 + G(x) + x = 0
Both F and G are functions, but F is in 'explicit' form because we have an explicit formula for its values. G is in 'implicit' form because for G(x) we do not have such an expression.
Of course the difference between the two notions is purely cosmetic and if you're cunning enough an implicit function can be written explicitly (although the expression we get might be rather messy). With the G example above it's possible to express G in terms of its inverse function, which is easily found.
Originally posted by SPMars A function is a function, whatever the situation.
Whether it's 'explicit' or 'implicit' is to do with how it's written down.
F(x) = 2x+9
G(x)^5 + G(x) + x = 0
Both F and G are functions, but F is in 'explicit' form because we have an explicit formula for its values. G is in 'implicit' form because for G(x) we do not have such an expression.
...[text shortened]... it's possible to express G in terms of its inverse function, which is easily found.
Originally posted by sonhouse So easily find it please.
Define a function H mapping R to R by
H(y) := -y^5-y
Since this is a strictly decreasing, continuous, bijection R -> R it has an inverse function G which is strictly decreasing and continuous and satisfies the relation G(x)^5+G(x)+x=0.
Furthermore, given x in R we have
G(x) = sup ( y: H(y) > x ).
But I don't expect you to understand the notation or the ideas I am using.
Originally posted by SPMars Define a function H mapping R to R by
H(y) := -y^5-y
Since this is a strictly decreasing, continuous, bijection R -> R it has an inverse function G which is strictly decreasing and continuous and satisfies the relation G(x)^5+G(x)+x=0.
Furthermore, given x in R we have
G(x) = sup ( y: H(y) > x ).
But I don't expect you to understand the notation or the ideas I am using.
Ok, what is 'bijection' and 'sup'? Terms I never heard of.