Use implicit differentiation to find the slope of the tangent line to the curve
{y/{x - 7 y} = x^{9} + 3
at the point ( 1, (4/29) ).

Question

anonymous · Answer

$$\frac{y}{x-7y}=x^9+3$$?

anonymous · Answer

yes that is the curve

anonymous · Answer

take the derivative implicitly. you need the quotient rule on the left. you should get 
$$\frac{(x-7y)y'-y(1-7y')}{(x-7y)^2}=9x^8$$

amistre64 · Answer

id kill the fraction and product rule it for a cleaner feel and a fresher scent

anonymous · Answer

do some algebra, plug in the numbers and solve for y'

anonymous · Answer

better idea!

anonymous · Answer

from grease to shine in half the time...

amistre64 · Answer

$$\frac{y}{x-7y}=x^9+3$$
$$y=(x^9+3)(x-7y)$$
$$y'=(x^9+3)'(x-7y)+(x^9+3)(x-7y)'$$
$$y'=(9x^8)(x-7y)+(x^9+3)(x'-7y')$$

anonymous · Answer

i definitely liked your second method better lol thank you!

anonymous · Answer

Thank you for explaining the first method too, figuring how to do it that way was killing me until you explained it

amistre64 · Answer

the quotient rule is inherently a nightmare ...