Question

3. Use implicit differentiation to find dy/da where 4x® - 7x*y2 = 3y - 6. Find the equation of the tangent line at the point (1, -1)

Answer 1

Note: page n-1 = na d Coc? da Pr Product. Rule : d (foogles) d. Pogos = [gco.crc)* |co diges (fgey) = f'(960) ogle) • Chain Rule :d oc)

6 page @ ; derivative en on both sides d (426 dlac d da da 4-1 (3-12 TA -X 3* tita da (chain nel) 5 3) Givern equation is 4x - 72 y = 34" - 6 Taking go wirte, we get 72 ) d(406) - dl ) - a (+ y) = d (344) - dll (2-1) 446€ to ody o] = 3,6y .3x4y dy {product rule] (chain rulla [-ray - 14xy day - 11 xy? - 24x 24** - alochy -ray 124² + 142 slope of the tangent point (1,-1) = dy = in => ma = 24-21 =-3 12(-1)3 + 14(*(-1) 26 Equation of tangent passing through through the point (any) is given as (y - y) = m(2-x), Raquered equation's (y+1)=21-1) dac 2.2 21' a 2 dy 24005 3 3 dac 14pé y line at de le- 24(4) – 21(15%-2)? -12-14 line with slope is