Recent questions in Implicit Differentiation

Implicit Differentiation
Answered

heelallev5
2022-08-05

$[{\mathrm{tan}}^{-1}(x){]}^{2}+[{\mathrm{cot}}^{-1}(y){]}^{2}=1$

Find the tangent line equation to the graph at the point (1,0) by implicit differentiation

I found the derivative:

$\frac{dy}{dx}}={\displaystyle \frac{4{\mathrm{tan}}^{-1}(x)\cdot {\mathrm{cot}}^{-1}(y)}{({y}^{2}+1)({x}^{2}+1)}$

I may have done my derivative wrong, but my main concern is at some point 0 will be plugged into cot inverse, resulting in division by zero.

Implicit Differentiation
Answered

Awainaideannagi
2022-07-28

$g(x)=3{x}^{-3}({x}^{4}-3{x}^{3}+15x-4)$

Implicit Differentiation
Answered

PoentWeptgj
2022-07-23

$-22{x}^{6}+4{x}^{33}y+{y}^{7}=-17$

and found it to be

$\frac{dy}{dx}}={\displaystyle \frac{132{x}^{5}-132{x}^{32}y}{4{x}^{33}+7{y}^{6}}$

Now, I am trying to find the equation of the tangent line to the curve at the coordinate (1,1). So I then plug both 1 in for x and y into the above equation and come up with

$\frac{0}{11}$

Now I go to solve

$y-y1=m(x-x1)$

getting

$y-1=0(x-1)$

resulting in $y=1$ and the equation to be $y=x+1$ for my final answer. Am I going about this in the correct manner?

Implicit Differentiation
Answered

Donna Flynn
2022-07-23

Implicit Differentiation
Answered

Donna Flynn
2022-07-23

The instructions ask me to find ${y}^{\prime}$, the problem is:

$(x-2y{)}^{3}=2{y}^{2}-3$

So far I've been able to get this far:

$3(x-2y{)}^{2}(1-2{y}^{\prime})=4y({y}^{\prime})$

I've been trying to manipulate it for a while but I can't figure out how to finish the problem properly.

Implicit Differentiation
Answered

Israel Hale
2022-07-23

As clarification an example I will provide an example:

Implicitly differentiate ${y}^{2}=x$.

You get

$2y\frac{dy}{dx}=1$

as one of the first steps in differentiation. Why is the $dy/dx$ added after ${y}^{2}$ is differentiated?

Implicit Differentiation
Answered

Taniya Burns
2022-07-22

${x}^{2}{y}^{2}-2xy+x=2$

find the slope and the equation of the tangent line at (2,0) by implicit differentiation.

Part of the problem is that my text book says find $d/dx$ and then ignore $dy/dx$ after I get

${x}^{2}{y}^{2}=2{x}^{2}y$

Please show me where I am going wrong. I would be able to find the equation of the tangent line if I had the correct ${f}^{\prime}(x)$

Implicit Differentiation
Answered

smuklica8i
2022-07-22

1.) ${x}^{3}-xy+{y}^{2}=4$

2.) $y=\mathrm{sin}(xy)$

find $\frac{{d}^{2}y}{d{x}^{2}}$

3.) ${x}^{2}{y}^{2}-2x=3$

Implicit Differentiation
Answered

kislotd
2022-07-22

$\frac{{x}^{2}}{x+y}={y}^{2}+6$

I know to take the derivatives of both sides and got:

$\frac{(x+y)2x-(1-\frac{dy}{dx}){x}^{2}}{(x+y{)}^{2}}=2y\frac{dy}{dx}$

I blackuced that to get:

$2{x}^{2}+2xy-{x}^{2}-{x}^{2}\ast dy/dx=(2y\ast dy/dx)(x+y{)}^{2}$

I then divided both sides by (2y*dy/dx) and multiplied each side by the reciprocals of the first three terms of the left side. Then I factoblack dy/dx out of the left side and multiplied by the reciprocal of what was left to get dy/dx by itself. I ended up with:

$dy/dx=(2y(x+y{)}^{2})/(4{x}^{7}y)$

but this answer was wrong. I only have one more attempt on my online homework and I can't figure out where I went wrong. Please help!

Implicit Differentiation
Answered

skilpadw3
2022-07-22

I have solved this in two ways.

First, I multiplicated the whole equation by $x+y$ and then I calculated the implicit derivative. I got the following solution:

$\frac{1-3{x}^{2}-2xy}{{x}^{2}+1}$

So far so good. When I calculated the implicit derivative of the original expression using the quotient rule though, I got a different solution, i.e.:

$-\frac{x(y+x{)}^{2}-y}{x}$

Can anyone explain to me why I get different solutions ?

Implicit Differentiation
Answered

Israel Hale
2022-07-22

$\frac{d}{dx}({e}^{x}({x}^{2}+{y}^{2}))$

I think its the $\frac{d}{dx}$ confusing me, I don't what effect it has compablack to $\frac{dy}{dx}$. Any help will be greatly appreciated.

Implicit Differentiation
Answered

Matilda Fox
2022-07-22

I am trying to use implicit differentiation to find dx/dy for this problem but the answer i keep getting is

$4x\mathrm{cos}(4x+5y)=-y\mathrm{sin}(x)$

and I am stuck.

Implicit Differentiation
Answered

Lorelei Patterson
2022-07-22

$\frac{\mathrm{\partial}z}{\mathrm{\partial}x}=\frac{-\mathrm{\partial}f/\mathrm{\partial}x}{\mathrm{\partial}f/\mathrm{\partial}z}$

if you have a function $z$ implicity defined by $f(x,y,z)=0$?

Implicit Differentiation
Answered

Zoagliaj
2022-07-21

The solution was as follows:

So if we derive with respect to $x$ we get

$8{x}^{3}{z}^{2}+4{x}^{4}z\frac{\mathrm{\partial}z}{\mathrm{\partial}x}=2x-4{y}^{5}z-4x{y}^{5}\frac{\mathrm{\partial}z}{\mathrm{\partial}x}$

Plugging inn $(1,-1,0)$ we get $\frac{\mathrm{\partial}z}{\mathrm{\partial}x}=\frac{1}{2}$.

But when we differentiate with respect to $x$, on the last expression they used the chain rule on $x$ and $z$ and treated $y$ as a constant. Shouldn't you also use the chain rule on $y$ and get something like $-4x{y}^{5}z-4x{y}^{5}\frac{\mathrm{\partial}z}{\mathrm{\partial}x}-20x{y}^{4}z\frac{\mathrm{\partial}y}{\mathrm{\partial}x}$.

I realize now that since $z=0$ in our point, the last expression would actually fall away and we would get the right answer. But the solution doesn't contain the last expression at all, so I'm confused about whether or not I've misunderstood implicit differentiation.

Implicit Differentiation
Answered

Makena Preston
2022-07-21

${x}^{3}+{y}^{3}=3xy.$

I have no idea how to do this, I didn't understand my lecturer. Can you guys show me the steps?

Implicit Differentiation
Answered

Arectemieryf0
2022-07-21

The hint is to use $y(t)/x(t)$ and use implicit differentiation but I can't see how to use that hint to solve this problem.

Implicit Differentiation
Answered

Luz Stokes
2022-07-20

Implicit Differentiation
Answered

Paxton Hoffman
2022-07-20

How do I solve this question? I know i have to solve for y' to find the gradient of the slope which I calculate to be y' = (2x-2)/(2y-4) y' = x-1/y-2

What do I do after this?

Implicit Differentiation
Answered

Matias Aguirre
2022-07-19

- 1
- 2