Posted by **lan** on Sunday, July 10, 2011 at 12:26am.

use implicit differentiation to find the slope of the tangent line to the curve (y)/(x-7y)=x^6+5 at the point (1,6/43)

- math -
**Reiny**, Sunday, July 10, 2011 at 12:35am
I would cross-multiply, then simplify to avoid using the quotient rule to get

36y = x^7 + 5x - 7x^6y

36dy/dx = 7x^6 + 5 -7x^6dy/dx - y(42x^5)

dy/dx(36 + 7x^6) = 7x^6 + 5x - 42yx^5

dy/dx = (7x^6 + 5x - 42yx^5)/(36+7x^6)

sub in x=1 and y = 6/43)

I will leave the arithmetic for you

- math -
**lan**, Sunday, July 10, 2011 at 4:23am
THANK YOU !

- math -
**Julie**, Tuesday, July 12, 2011 at 10:23pm
when you cross multiply how do you get 36y?

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