Implicit differentiation

[yanarains]

Given 12x2 + y2 = 21

Use implicit differentiation to find dy/dx and evaluate it at (1, 3)

My work:

(24x+2y)dy/dx=0

dy/dx= -x/y= -1/3=-.333

What is the correct way to solve this equation?

Thank you

 

[Deleted member 4993]

Given 12x2 + y2 = 21

Use implicit differentiation to find dy/dx and evaluate it at (1, 3)

My work:

(24x+2y)dy/dx=0

dy/dx= -x/y= -1/3=-.333

What is the correct way to solve this equation?

Thank you

You need to review this part:

\(\displaystyle \frac{d}{dx} (12x^2+y^2)\)

= \(\displaystyle 24x + 2y\cdot\frac{dy}{dx}\)

then

\(\displaystyle 24x + 2y\cdot\frac{dy}{dx}\) = 0

\(\displaystyle \frac{dy}{dx}\) = -\(\displaystyle 12\cdot\frac{x}{y}\)

Now evaluate \(\displaystyle \frac{dy}{dx}\)

 

[Dr. Flim-Flam]

Given: 12x²+y² = 21, find the slope at (1,3).

24x+2yy' = 0, 2yy' = -24x, y'=-24x/2y = -12x/y, = -4 at (1,3).

Note: Can also be solved explicitly, to wit:

y² = 21-12x², y = ±√(21-12x²), y'=-24x/2±√(21-12x²) = -12x/±√(21-12x²).

When x = 1, y' = -12/±3 = -4 or 4. Disregard 4 (extraneous solution).