Math (Calculus)
posted by Alex .
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?
I don't understand

puzzled, why would your write the point as
(1 , 1/8) and not as simply (1 , 1/8) ?
first expand it
y = x^7  2x  9x^6 y + 18y
0 = x^7  2x  9x^6 y + 17y
0 = 7x^6  2  9x^6 dy/dx  54x^5y + 17dy/dx
dy/dx(17  9x^6) = 54x^5y  7x^6
dy/dx = (54x^5y  7x^6))/(17  9x^6)
at x = 1
dy/dx = (54(1/8) 7)/(17  9)
= (1/4) / 8
= 1/32
equation of tangent:
y + 1/8 = (1/32)(x1)
y = (1/32)x + 1/32  1/8
y = (1/32)x 3/32
check my arithmetic
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