If ln(x^2−8y)=x−y+4 and y(−3)=1, find y′(−3) by implicit differentiation.

Question

If ln(x^2−8y)=x−y+4 and y(−3)=1, find y′(−3) by implicit differentiation.

y′(−3)=

An equation of the tangent line to the curve at the point (−3,1) is

y=

.

Answer 1

(2x - 8y^’)/(x² - 8y) = 1 - y^’. @ ( - 3 , 1 )

( -6 - 8y^’) = 1 - y^’

7y^’ = -7

y^’(-3) = -1

Eqn of tan line: y = -1(x + 3) + 1