Friday

August 22, 2014

August 22, 2014

Posted by **Kim** on Friday, November 6, 2009 at 12:10am.

Use implicit differentiation to find the slope of the tangent line to the curve at point (4,1).

y / (x-2y) = x^3 + 4

Tried quotient rule to get the derivative of the left side, then got derivative of right side, and ultimately I got y + 3x^2 (x-2y)^2 / x-2y-2y

This is clearly not correct since the bottom would turn into zero if I plugged in x and y. Sigh...

- calculus -
**drwls**, Friday, November 6, 2009 at 5:21amIt will be easier if you multiply it out and combine terms.

9y = x^4 +4x -2x^3 y

Differentiate both sides with respect to x implicitly, treating y as a function of x.

9 dy/dx = 4x^3 + 4 -2x^3 dy/dx

-6x^2 y

dy/dx(9 + 2x^3) = 4x^3 + 4 - 6x^2 y

dy/dx = [4x^3 -6x^2 y +4]/(9 + 2x^3)

Plug in x=4 and y=1. You should not get a zero deniminator.

**Related Questions**

Implicit Differentiation - Use implicit differentiation to find the slope of the...

calculus; implicit differentiation - Use implicit differentiation to find the ...

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...

Calculus - Use implicit differentiation to find the slope of the tangent line to...

Calculus Please help! - Use implicit differentiation to find the slope of the ...

Math (Calculus) - Use implicit differentiation to find the slope of the tangent ...

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 ...