Equation of tan line helppp

Question

if x^3+3y^5+2x=3y^7+2x^2+4 Find the equation of tangent line at (2,1)

Answer 1

the eqn of tangent line simple means the slope of the line.

x^3+3y^5+2x=3y^7+2x^2+4 is the same as



x^3+3y^5+2x-3y^7-2x^2 = 4

slope = dy/dx

differentiate the eqn implicitly

3x^2 +15y^4dy/dx +2 - 21y^6 dy/dx -4x =0

notice that all the terms with y have a dy/dx attached to them(that's how implicit differentiation works, cos were differentiating wrt x and not y)

15y^4dy/dx - 21y^6dy/dx = -3x^2 +4x-2

dy/dx = (-3x^2 +4x-2)/(15y^4 - 21y^6)

plug in x=2 and y=1

and ur ans=dy/dx=slope

eqn of a line: y=Mx +c

where M is the slope