For questions on finding and evaluating derivatives when a function is defined implicitly.
Questions tagged [implicit-differentiation]
1329 questions
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Derivative of implicit functions
This problem got me confused. I'm supposed to find the value of the derivative of $$y\mathrm{e}^y=\mathrm{e}^{x+1}$$ at the point $x=0$.
I did find the derivate but I can't find its value because the derivate is $$\frac{y}{y+1}.$$ So basically there…
E.Buzi
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Differentiate $y = 2^x + 2^{-x}$
I have a question about negative powers in implicit differentiation.
I was asked to differentiate the equation
$$y = 2^x + 2^{-x}$$
Now, from previous studies, I can prove the following:
$y = a^x$
$\ln y = \ln a^x = x \ln a$
$\frac{1}{y}…
vik1245
- 893
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1 answer
Differentiation problem probably using increasing or decreasing property of differentiation
Let $f:\mathbb{R} \to \mathbb{R}$ be twice differentiable function on $\mathbb{R}\setminus\{p\}$, for some $p$ belonging to $\mathbb{R}$. If $f'(x)<00 >f''(x)$ on $x>p$, then $f$ is not differentiable at $p$.
user476538
- 103
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2 answers
Use implicit differentiation to find $\frac{dc}{dv}$ when $c=\sqrt{c^2+v^2}$
Use implicit differentiation to find $\frac{dc}{dv}$ when $v=\sqrt{c^2+v^2}$
I know I can solve this using normal implicit methods however I was wondering, why can I not square this so it becomes $v^2=c^2+v^2$ and then simplify so $ c^2=0…
bigfocalchord
- 5,597
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Second order differentiation
Differentiating dy/dα w.r.t x what would we get?
The textbook i'm using says the answer is (d^2y/dα^2)(dα/dx) but I'm not able to understand it.
Sidd
- 11
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Implicit Function and partial derivatives
Not sure how to interpret this question or where to start.
$\text{Assuming that the equation}$ $$F(x,y,z) = 0$$ $\text{defines} z \text{implicitly as a differentiable function of} \: x \: \text{and} \: y \: \text{and that}$ $$F_{zx} = F_{xz}$$…
Twenty-six colours
- 1,881
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Implicit Differentiation under conditions
Consider the equation $z^2-1=x^3y$.
Find the value of $\frac{dy}{dt}$ under these conditions $z=5,x=2,y=3, \frac{dx}{dt}=-2$ and $\frac{dz}{dt}=7$.
So I'm not really getting this. I think what I do is take the derivative of the original so I get…
Ernie
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2 answers
Why can we define y as a function of x in implicit differentiation?
I understand the method used in implicit differentiation, it's just an application of the chain rule. But why can you define $y$ as a function of $x$?
In this equation for example:
$x^2 + y^2 = 1$
$2x + 2yy' = 0 $
Why isn't it just this?:
$2x +…
SadSeven
- 193
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2 answers
Implicit differentiation for the given equation
Determine the first and second derivative of $y$ being given the equation
$x^5+y^5-15=0$
David David
- 62
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1 answer
Implicit differentiation with 2 unknowns
$xy(x - 6y) = 9a^3$ , a is not 0
The Question
Show that there is only one point on the curve at which the tangent is parallel to the x axis, and find the coordinate of this point.
How would I go about solving this question?
codez
- 187
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1 answer
What is the dirctional derivative of a norm?
Usually norm is not differentiable function. But norm has directional derivative.
What is the form dirctional derivative of a norm in a direction d?
0
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2 answers
What is the slope of the tangent line to the curve sin(πx)+ln(x^2)y+sec(πx)=xy at x=1?
sin(πx)+ln(x^2)y+sec(πx)=xy
How am I supposed to sub in x=1 if I don't know what y is? I got:
dy/dx = y-(2y/x)-πcos(πx)-πsec(πx)tan(πx)/(2ln(x)-x)
But then how do I solve this question if I got dy/dx or is that not what I was supposed to…
John Smith
- 27
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2 answers
Implicitly differentiate $sqrt(x+y) = 3x$ without squaring both sides first?
I was just curious about how I could implicitly differentiate $sqrt(x+y) = 3x$ without squaring both sides first. Obviously, if I square both sides first, it becomes "easier" to differentiate and I get:
$dy/dx = 18x-1$
However, whenever I try and…
ZERO
- 35
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3 answers
Using Implicit Differientation to find a formula for dy/dx
I already have all the steps down, one thing I couldn't understand was how to get the final answer (which I have also):
The equation given is $y=xe^y$
Here is the steps I've taken so far:
$\frac{d}{dx}y=xe^{y}$
$\frac{dy}{dx}=\frac{d}{dx}e^y * x +…
Andy Le
- 9
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1 answer
Basic Implicit Differentiation
The curve C has equation $2x^2 + y^2 =18$. Determine the coordinates of the four points
on C at which the normal passes through the point $(1, 0)$.
Here's what I did:
And,
$m_{normal} = \frac{y}{2x}$
But then here's where I get stuck - when I…
StopReadingThisUsername
- 1,553