What is the slope of the tangent line to this curve at the point (2,2)?

Question

(9*x^2*y+10*x)/(8*y-3*x^3)

What is the slope of the tangent line to this curve at the point (2,2)?

The equation of the tangent line to this curve at this point is

y=?

Answer 1

(9 x^2 y + 10 x)

---------------- is the original function

7 y - 3 x^3

Quotient rule:

(7 y - 3 x^3) (18x y + 9 x^2 y' + 10) - (9x^2 y + 10x) (7 - 9x^2)

------------------------------------------------------------------

7 y' - 9x^2

Plugs in (2,2)

(7*2 - 3*2^3) (18*2*2 + 9*2^2 y' + 10) - (9 *2^2 *2 + 10*2)(7 - 9 2^2)

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7 y' - 9 2^2

(14 - 3*8)(72 + 36y'+10) - (9*4*2 + 20)(7 - 9*4)

------------------------------------------------

7 y' - 9*4

(-10)(82 + 36 y') - (72+20)(7 - 36)

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7 y' - 36

-360 y' - 820 - (-31)(92)

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7 y' - 36

-350 y' - 820 + 2852

----------------------

7 y' - 36

-350 y' + 2032

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7 y' - 36