Thursday
October 23, 2014

Homework Help: Calc, Implicit Differentiation

Posted by Michael on Saturday, October 21, 2006 at 7:28pm.

Regard y as independent variable and x as dependant variable and find the slope of the tangent line to the curve (4x^2 + 2y2)^2 - x^2y = 4588 at point (3,4).

Correct answer is -0.668827160493827

Here's what I did:

2(8x(dy/dx) + 4y) -2x(dx/dy)y + x^2 = 0
16x(dx/dy) + 8y - 2x(dx/dy)y = -x^2
16x(dx/dy) - 2x(dx/dy)y = -x^2 - 8y
(dx/dy)(16x -2xy) = -x^2 - 8y
(dx/dy) = (-x^2 - 8y)/(16x -2xy)

But this doesnt work.


You have
(4x2 + 2y2)2 - x2y = 4588
It appears you started correctly and you know what you want, dy/dx, but I don't think you did the correct calculations.
It might help to think of this as
(f(x) + g(y))2 - h(x)*y = C
where f(x) = 4x2, g(y)=2y2 and h(x)=x2.
Then the differentiation should go
2(f(x) + g(y))*d/dx(f(x) + g(y)) - h(x)*dy/dx -h'(x)y = 0
Then f'(x)=8x, d/dx g(y)=g'(y)*dy/dx and h'(x)=2x
What I suggest, and this what I've done for real long expressions, is to write the symbols out, do the differentiation on the symbols, then substitute them into your equation.
Does this help?

Answer this Question

First Name:
School Subject:
Answer:

Related Questions

Calculus - Regard as the independent variable and as the dependent variable and ...
calculus - Regard y as the independent variable and x as the dependent variable ...
Implicit Differentiation - Use implicit differentiation to find the slope of the...
Math - Use implicit differentiation to find the slope of the tangent line to ...
Math - Use implicit differentiation to find the slope of the tangent line to ...
Calculus ap - Use implicit differentiation to find the slope of the tangent line...
Calculus - (y/(x+9y))= (x^2)-7 at the point (1, -6/55) Use implicit ...
Calculus - Use implicit differentiation to find the slope of the tangent line to...
math - use implicit differentiation to find the slope of the tangent line to the...
CAL - use implicit differentiation to find the slope of the tangent line to the ...

Search
Members