For questions on finding and evaluating derivatives when a function is defined implicitly.
Questions tagged [implicit-differentiation]
1329 questions
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Implicit Differentiation Undefined Gradient
Find the equation of the tangent to the curve for the following equation at the point $(2, -3)$
$$4x^2-3xy-y^2=25$$
$$\therefore8x-3x\frac{dy}{dx}-3y-2y\frac{dy}{dx}=0 $$
$$\therefore\frac{dy}{dx} =…
StopReadingThisUsername
- 1,553
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Separable DE Substitution
Hi I'm trying to solve a separable DE with a worked solution.
Question:
$y′ = (y−9x)^2$
Part of the Given Solution:
Letting $v = y − 9x$
becomes $\frac{dv}{dx} = v(x)^2 − 9$
I get that $\frac{dv}{dx} = \frac{dy}{dx} - 9$ but how does the…
Chris
- 21
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1 answer
How to tell the monotonicity from the implicit expression
I have an equation as $f(x,y)=0$, and $f$ is very complicated that there is no way to rewrite it as $y=g(x)$ explicitly.
I would like to show that $y$ is increasing at $x$, is there any way I can show this from $f(x,y)=0$ instead of the classic ways…
Jingjings
- 295
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0 answers
Implicit functions differentiation
While differentiating an implicit function , I ended up treating du/dx as a fraction and I am not quite happy about that . I want to know whether it's mathematically accurate to do that .
Question: Differentiate x(y)^3 with respect to x by not using…
Abu Bardewa
- 411
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1 answer
Trouble following simplification stage of implicit differentiation problem - basic question
Show that the equation of the tangent at the point $(x_1,y_1)$ to the curve with equation $x^2-2y^2-6y = 0$ is $xx_1-2yy_1-3(y+y_1)=0$
Alright I'm having a problem following an example from my textbook. I'll just show what I do follow and then…
Rogerc1979
- 219
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2 answers
Implicit Differentiation of $\sqrt{\frac{x}{y}} + \sqrt{\frac{y}{x}} = 6$
Find $\frac{dy}{dx}$ when $\sqrt{\frac{x}{y}} + \sqrt{\frac{y}{x}} = 6$.
Xoque55
- 4,384
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3 answers
Implicit differentiation q
Show that the sum of the x and y intercepts of any tangent line to the curve
$x^{1/2} + y^{1/2} = 4$ is equal to 16
So far I have found the derivative, $-\frac{\sqrt{y}}{ \sqrt{x}}$, but am having trouble as to how I would found the point of…
Rebecca
- 15
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1 answer
Is this a valid way of computing the implicit derivative?
Suppose I wish to compute the implicit derivative of $\sqrt{x^2+y^2}=x+y$. One could differentiate both sides with respect to $x$, yielding $y\prime$ which we can make the subject.
Say I were to first square both sides, getting the expression…
Trogdor
- 10,331
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1 answer
Implicit differentiation, what am I doing wrong?
The problem is as follows:
$y^2(2-x)=x^3$
I know now how to solve it. However, my first try is described underneath, and I still do not know why that did not work. Could anyone explain it to me. I hope I did not do some horrible mistake…
Akitirija
- 435
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3 answers
Use implicit differentiation to find the largest y-value in the loop of the Folium of Descartes, which is given by :$ x^3 + y^3 - 3xy = 0$.
My professor didn't even explain how to do this. I asked the TA,and they told me to equal the first derivative to $0$ and solve for $x$ and then see if the second derivative is less than $0$? Can someone explain this problem to me?
Elsa
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Implicit Differentiation, $\frac{dy}{dx}$, parallel tangent
A curve has equation $x^2 - 4xy + 2y^2 = 1$.
a) Find ad simplify an expression for $\frac{dy}{dx}$.
b) Show that the tangent to the curve at the point $P=(1,2)$ has the equation
$$3x - 2y +1 = 0.$$
The tangent to the curve at the point $Q$ is…
Vales
- 1
-1
votes
1 answer
Is there an order to approaching implicit differentiation questions?
For example, I have the question "solve for $\frac {dy}{dx}$: $$ycos(xy)=y^2+2"$$ and I'm not sure if I should differentiate with the product rule or the chain rule first for the left side of the equation.
I apologize if this is a question with an…
ilya.te
- 13
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1 answer
Implicit differentiating vxcosx^2
I have been trying to implicitly differentiate $$y = 2vx\cos (x^2)$$, where y, v and x are variables. All I need to know is how to differentiate$$ 2vx\cos(x^2)$$ implicitly.
What I am thinking if is that, by using product rule I will need to…
-1
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1 answer
Challenging differentiation problem
I am trying to do it with substitution and getting a $1$ as answer but the answer is $\ln (4e^2)$
Given:
$$ y = (1 + \frac{1}{x})^x + x^{1+\frac{1}{x}}$$
Evaluate $y'(1)$
Akshat
- 9
-1
votes
1 answer
Implicit differentiation
The equation of a curve is $xy(x + y) = 2a^3$ , where $a$ is a non-zero constant. Show that there is only
one point on the curve at which the tangent is parallel to the x-axis, and find the coordinates of this
point.
I am completely lost.
Riduan Gonzalez
- 179