SOLUTION: 1. Differentiate f(x) = {square-root of [(x-1) divided by (x+1)]}. 2. Differentiate (2y-x)^6 + x^3 = y = 3. 3. Evaluate the derivatives of the function at the point 3x^3

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Question 840705: 1. Differentiate f(x) = {square-root of [(x-1) divided by (x+1)]}.
2. Differentiate (2y-x)^6 + x^3 = y = 3.
3. Evaluate the derivatives of the function at the point
3x^3y^2 - 2y3 = -3; (1,2). thank you so much.
Found 2 solutions by Edwin McCravy, AnlytcPhil:
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
* A shherical balloon is being inflated. Find the expression for the
instantaneuos rate of change of the volume with respect to the radius.
Evaluate this rate of change for the radius of 4.00m using the delta
process.
The formula for the Volume is 

But we must NOT substitute 4 for r until after we have
found the derivative, since r is still a variable until 
we "freeze" r at the instant when r is 4.
I am using Dx for Dx 
 =
 
 =
 =
 =
 =
 =
 = 

 =
 =
 =
 =

Finally, we substitute r = 4
 =
 =

find the derivative of the implicit function [3x^2
divided by (y^2 + 1) plus y= 3x + 1]
Use the quotient formula for the first expression
Remember that although the derivative of x is 1, the
derivative of y is NOT 1 but 


Multiply through by the denominator (y²+1)²





 

 

 
 
That's as far as I'm taking it.  You can multiply all that out
if you like.  There is no sense in any teacher giving you a
problem that comes out so messy and unwieldy as that!

Edwin
Answer by AnlytcPhil(1806)   (Show Source): You can put this solution on YOUR website!

1. Differentiate f(x) = {square-root of [(x-1) divided by (x+1)]}.

2. Differentiate (2y-x)^6 + x^3 = y = 3.
I'll assume that last equal sign was a typo and should be a +,
and that you meant

2. Differentiate (2y-x)^6 + x^3 = y + 3.






Solve for

3. Evaluate the derivatives of the function at the point
3x^3y^2 - 2y3 = -3; (1,2). thank you so much.






Solve for 













Substitute (x,y) = (1,2).

 

Edwin
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