implicit differentiation Definition and Topics - 15 Discussions
In mathematics, an implicit equation is a relation of the form R(x1,…, xn) = 0, where R is a function of several variables (often a polynomial). For example, the implicit equation of the unit circle is x2 + y2 − 1 = 0.
An implicit function is a function that is defined by an implicit equation, that relates one of the variables, considered as the value of the function, with the others considered as the arguments. For example, the equation x2 + y2 − 1 = 0 of the unit circle defines y as an implicit function of x if –1 ≤ x ≤ 1, and one restricts y to nonnegative values.
The implicit function theorem provides conditions under which some kinds of relations define an implicit function, namely relations defined as the indicator function of the zero set of some continuously differentiable multivariate function.
Let $$Y(t)=tanh(ln(1+Z(t)^2))$$ where Z is the Hardy Z function; I'm trying to calculate the pedal coordinates of the curve defined by $$L = \{ (t (u), s (u)) : {Re} (Y (t (u) + i s (u)))_{} = 0 \}$$ and $$H = \{ (t (u), s (u)) : {Im} (Y (t (u) + i s (u)))_{} = 0 \}$$ , and for that I need to...
Summary:: van der waals
I have a pretty good understanding of implicit differentiation. However I'm stuck on a homework problem and could use some help.
[P + (an^2)/V^2][V - nb] = nRT a,n,b,R are constants
My professor wants me to take the implicit differentiation of P wrt...
Homework Statement
Find the value of h'(0) if: $$h(x)+xcos(h(x))=x^2+3x+2/π$$
Homework Equations
Chain Rule
Product Rule
The Attempt at a Solution
I differentiated both sides, giving h'(x)+cos(h(x))-xh'(x)sin(h(x))=2x+3
Next I factored out and isolated h'(x) giving me...
Hello. My problem is as follows: Suppose x^4+y^2+y-3=0. a) Compute dy/dx by implicit differentiation. b) What is dy/dx when x=1 and y=1? c) Solve for y in terms of x (by the quadratic formula) and compute dy/dx directly. Compare with your answer in part a).
I solved a) and b). a)=-4x^3/2y+1, and...
The following lines of codes implements 1D diffusion equation on 10 m long rod with fixed temperature at right boundary and right boundary temperature varying with time.
xsize = 10; % Model size, m
xnum = 10; % Number of nodes
xstp =...
Homework Statement
Hello
I have this circle with the equation : [/B]
(x-a)^2+(y-b)^2=r^2
I want to find dy/dx for it
2. Homework Equations
(x-a)^2+(y-b)^2=r^2
The Attempt at a Solution
I am looking on the internet and it appears that I should use what is called "Implicit differentiation"...
For implicit differentiation, is dy/dx of x2+y2 = 50 the same as y2 = 50 - x2 ?
From what I can take it, it'd be a no since.
For x2+y2 = 50,
d/dx (x2+y2) = d/dx (50) --- will eventually be ---> dy/dx = -x/y
Where,
y2 = 50 - x2
y = sqrt(50 - x2)
dy/dx = .5(-x2+50)-.5*(-2x)
Homework Statement
Find the equation of the tangent line to the curve ##\ xy^2 + \frac 2 y = 4## at the point (2,1).
Answer says ##\ y-1 = -\frac 1 2(x-2)##
And with implicit differentiation I should have gotten ##\frac {dy} {dx}= -\frac {y^2} {2xy-\frac {2} {y^2}}##
Homework Equations
##\...
<< Mentor Note -- thread moved from the technical math forums at OP request, so no Homework Help Template is shown >>
x2y + xy2 = 6
I know we use the chain rule from here, so wouldn't that be:
(d/dx)(x2y + xy2) = (d/dx)(6)
so using the chain rule of g'(x)f'(g(x) and the d/dx canceling out on...
First of all thanks for the help, i have a problem finding a good explanation of de ecuation (d/dx)f=(∂f/∂x)+(∂f/∂y)*(dy/dx) could anyone write me a good explanation of this ecuation? thanks for the help
Homework Statement
with answers given:
Homework Equations
use implicit differentiation
The Attempt at a Solution
I always get this answer
but not the second one
PLs explain the second answer for I am very desperate.
Thank You
I unfortunately keep on getting the wrong answer to this problem.
I am supposed to find: dw/dy(1/(w^2+x^2)+1/(w^2+y^2))
I attached a picture of how I tried to solve it. Help would be much appreciated.
< Moderator Note -- Thread moved from the technical PF Calculus forum >
I can't seem to grasp the idea of this problem, any help is much needed. The problem reads, "As a spherical raindrop falls, it reaches a layer of dry air and begins to evaporate at a rate that is proportional to its...