Question

if7y−2y5−2x+3x3−25=0,finddydxat(2,1).

Hence, find the equation of the line tangent to the curve at this point?

Answer 1

use implcicit differentiation

Answer 2

\[\frac{dy}{dx}=y^{'}\]
\[7y^{'}-2(5)y^{'}y^4-2+9x^2=0\]

Answer 3

\[\frac{ dy }{dx }(7-10y ^{4})=2-9x ^{2}\]

Answer 4

yes

Answer 5

\[dydx=\frac{ 2−9x2 }{ 7−10y4 } ???\]

Answer 6

yes did you understand the procedure on how to use implicit diff

Answer 7

from here put (2,1)

Answer 8

\[\frac{ 2-9(2)^{2} }{ 7-10(1)^{4} }=\frac{ 34 }{ 3 }\]

Answer 9

yes that's your gradient m=34/3
so nw use y-y1=m(x-x1)

Answer 10

\[y=\frac{ 34 }{ 3 }x-\frac{ 68 }{ 3 }+1= \frac{ 34 }{ 3 }x-\frac{ 65 }{ 3 }\]