calculus

posted by .

Use implicit differentiation to find the slope of the tangent line to the curve (y/x+8y)=x^8 +9 at the point (1,10/-79).

• calculus -

I would rather use the product rule than the quotient rule, so lets multiply each term by x to get
y + 8xy = x^9 + 9x
dy/dx + 8x(dy/dx) + 8y = 9x^8 + 9
dy/dx(1+8x) = 9x^8 + 9 - 8y
dy/dx = (9x^8 + 9 - 8y)/(1+8x)

plug in your point and you are done.

Similar Questions

1. calculus; implicit differentiation

Use implicit differentiation to find the slope of the tangent line to the curve at the point (4,1) -1x^2 - 4xy + 3y^3 = -29 I differentiated both sides and solved for dy/dx and got 2x-4y/9y^2-4x. Then I plugged in X and Y and got -4/7 …
2. Calculus

Use implicit differentiation to find the slope of the tangent line to the curve –2x^2–2xy–1y^3=–3 at the point (–1–1).
3. Calculus

Use implicit differentiation to find the slope of the tangent line to the curve 2(x^2) + 2xy + 2(y^3)= -18
4. Calculus

(y/(x+9y))= (x^2)-7 at the point (1, -6/55) Use implicit differentiation to find the slope of the tangent line to the curve
5. Implicit Differentiation

Use implicit differentiation to find the slope of the tangent line to the curve y/x+6y=x^2–6 at the point (1,–5/31) . Again i think i'm messing up with the algebra here. I used quotient rule to get [(x+6y)(y')-(y)(1+6y')]/(x+6y)^2=2x …
6. Calculus AP

implicit differentiation Find the slope of the tangent line to the curve xy^3 + 2y - 0.76 =0 at the point (-3, o.7) I'm lost. so 3xy^2 * y' + 2y = 0 right?
7. Calculus ap

Use implicit differentiation to find the slope of the tangent line to the curve XY^3 + XY = 5 at the point (3,2) .
8. Math (Calculus)

Use implicit differentiation to find the slope of the tangent line to the curve y/(x–9y)=x^6–2 at the point (1,-1/-8). Can someone please help me?