For questions on finding and evaluating derivatives when a function is defined implicitly.
Questions tagged [implicit-differentiation]
1329 questions
0
votes
1 answer
Implicit partial derivative of wave function
I'm working out some QM problems and need to clarify the procedure for calculating the partial of an implicit function. What's needed is to differentiate a wave function twice with respect to t. Here's the function: $φ(x,t) = e^{i(ax − bt)}ψ(x −…
0
votes
1 answer
Finding partial derivatives using differentials in a system of equations
This homework exercise comes from M. Boas, Mathematical Methods in the Physical Sciences:
Typed out:
If $xs^2+yt^2=1$ and $x^s+y^2t=xy-4$, find $\partial x/\partial s$, $\partial x/\partial t$, $\partial y/\partial s$, $\partial y/\partial t$, at…
Erik
- 83
- 7
0
votes
2 answers
Derivative of $x^{y^z} + y^{x^z}$ with respect to $z$
Please what is the partial derivative of $x^{y^z} + y^{x^z}$ with respect to $z$
I guess this is not ${(x^y)}^z$ but rather $x^{(y^z)}$ so I tried using the logarithm function and found
$\ln x\ln y(x^{y^z} y^z+y^{x^z} x^z)$
But I don't know if I…
arsene stein
- 409
0
votes
0 answers
Implicit differentiation, its derivative
I'm unsure how the derivative comes out in the following. I have a parametrization $t'=f(t)$ and a parameter $x(f(t))$ and I'm taking: $\frac{d}{d(f(t))}x(f(t))$. I'm not sure if the derivative would come out as
$ \frac{df(t)}{dt} \frac{d}{dt}x(t)…
Linus
- 51
0
votes
3 answers
Problem with differentiation question
The question is as follows:
Let $l$ be any tangent to the curve $\sqrt{x}+\sqrt{y} = \sqrt{k}$, where $k > 0$. Show that the sum of the $x$-intercept and the $y$-intercept of $l$ is $k$.
0
votes
2 answers
Implicit Differentiation - Logarithm
$x\log(x) + y\log(y) = 1$
$\dfrac{dy}{dx}= ?$
I calculated $\frac{dy}{dx}= -\frac{1+\log(x)}{1+\log(y)}$
however, the correct answer seems to be $-\log(x)/\log(y)$
I'm confused, can someone help?
0
votes
1 answer
I'm differentiating this wrong!
I am self-teaching calculus and have been looking at the related rates practice problems here: https://www.whitman.edu/mathematics/calculus_online/section06.02.html
I am having trouble with the last problem, which relates to the rate at which a…
0
votes
2 answers
Implicit differentiation at a point with trigonometry and a fraction.
Find $\frac{dy}{dx}$ for $xcosy-2sin(\frac{y}{2})=0$ at (2,$\frac{\pi}{3}$)
I tried using the power rule and chain rule but I do not seem to solve the problem. Can someone tell me how to solve it?.
ac1002
- 141
0
votes
1 answer
Implicit Differentiation: Demand
Does anybody know how to solve this??
A price $p$ (in dollars) and demand $x$ for a product are related by
$2x^2+2xp+50p^2=20600$.
If the price is increasing at a rate of 2 dollars per month when the price is 20 dollars, find the rate of change of…
Peter Ferri
- 49
0
votes
1 answer
A Business Problem
A manufacturer produces bolts of a fabric with a fixed width. A quantity $q$ of this fabric (measured in yards) that is sold is a function of the selling price $p$ (in dollars per yard), so we can write $q=f(p)$. Then, the total revenue earned with…
Peter Ferri
- 49
0
votes
1 answer
Implicit Differentiation: Quadrifolium
The Question is:
Let $(x^2+y^2)^3=(x^2-y^2)^2$ be a curve. Find the points on the curve where the normal line is parallel to y=0.
I have $\dfrac{dy}{dx}=\dfrac{-x(3x^4+6x^2y^2+3y^4-1)}{y(3x^4+6x^2y^2+3y^4+1)}$= a/0
as the slope of the normal line…
Peter Ferri
- 49
0
votes
2 answers
Implicit Differentiation: Finding points Parallel to y=-x
The Question asks:
Let $x^{2/3}+y^{2/3}=2$ be a curve. Find points on the curve where the tangent line is parallel to $y=-x$.
I have got to $\dfrac{dy}{dx} = -\dfrac{x^{-1/3}}{y^{-1/3}}$ but am confused about how to find the points.
Peter Ferri
- 49
0
votes
2 answers
Consider the curve C given by $(x^2+y^2)^2=(x^2−y^2)$
Consider the curve C given by $(x^2+y^2)^2=(x^2−y^2)$
Using implicit differentiation, find $dy/dx$ in terms of $x$ and $y$.
Find all points $(x,y)$ on $C$ such that the tangent line is horizontal. You may assume $(x,y)≠(0,0)$
What is the smallest…
Ruby Liu
- 1
0
votes
2 answers
The equation of the normal when the gradient of the tangent = 0
Q. Find the equation of the tangent and normal to $x^2-xy+y^2 = 3$ at $(1,2)$.
I have done the first part. I found:
$$\displaystyle\frac{dy}{dx} = \displaystyle\frac{y-2x}{2y+x}$$
and substituted $x = 1$ and $y = 2$.
I found the gradient to be 0.
I…
Juan Pablo
- 187
0
votes
2 answers
Find $\frac{dy}{dx},$ if $x\sqrt{1-y}+y\sqrt{1-x}=0$
If $x\sqrt{1-y}+y\sqrt{1-x}=0$, then show that $\frac{dy}{dx}=\frac{-1}{(1+x)^2} $.
Attempt:
On differentiating both sides w.r.t x, I got the following result, which doesn't match with the expected expression.
$$\frac{d}{dx} \{ x\sqrt{1-y} +…
Shukant Pal
- 231