Implicit Differentiation: two different answers

funlord
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Homework Statement



upload_2015-8-12_21-14-47.png

with answers given:

upload_2015-8-12_21-15-58.png

Homework Equations


use implicit differentiation

The Attempt at a Solution


I always get this answer

upload_2015-8-12_21-17-54.png

but not the second one

PLs explain the second answer for I am very desperate.
Thank You
 

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Use what you begin with i.e. ##(x-y)^3 = (x+y)^2## inside the expression you get from implicit differentiation

Show your steps
 
funlord said:

Homework Statement



View attachment 87235
with answers given:

View attachment 87236

Homework Equations


use implicit differentiation

The Attempt at a Solution


I always get this answer

View attachment 87237
but not the second one

PLs explain the second answer for I am very desperate.
Thank You
Please state the entire problem.
 
funlord said:

Homework Statement



View attachment 87235
with answers given:

View attachment 87236

Homework Equations


use implicit differentiation

The Attempt at a Solution


I always get this answer

View attachment 87237
but not the second one

PLs explain the second answer for I am very desperate.
Thank You

In order to get the second answer, you need to take the ln of both sides of the equation, then differentiate implicitly. After rearranging, if done right (presumably the second answer is correct), you should have the same answer.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

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