**Q: Using implicit differentiation, find dy/dx of**

** y/(x+6y)=x**^{7}-9

**at the point (1,-8/49)**

A:

Taking the derivative of the right side of the equation is fairly basic, taking the derivative of the left side, on the other hand, is harder. The left side involves a quotient rule. I am going to ignore the right side of the equation for now and just deal with the left:

**y/(x+6y)**

The quotient rule tells you (in some form / notation or another):

(bottom)*(deriv. of top) – (deriv of bottom)*(top) all divided by (bottom) squared. **[You may have learned this with f’s and g’s and f ‘ and g ‘ — it all says the same thing]**

So:

Top = y

Bottom = x + 6y

Derivative of Top = dy/dx = y’ [whatever notation you are using]

Derivative of Bottom = 1 + 6(dy/dx) = 1 + 6y’

Continue reading Implicit Differentiation

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