Have you learnt implicit differentiation?

Yes, the thing is, I know but I'm not sure wjat the question is asking for. Do I sub in the x and y, then differenciate, or differenciate first then sub x and y in. The problem here is I don't understand the qn.

Differentiate first, then sub values in.

If you sub in first, there won't be anything to differentiate... You'll obtain constants on both sides and you would just be verifying that the LHS = RHS

i.e the point (2,1) satisfies the equation.

I'll type out the answer, you see if you can understand

ln y + eˣ + 2 = xy + e²

Perform implicit differentiation with respect to x

(d/dy (ln y) ) dy/dx + d/dx (eˣ) + d/dx (2) = x (d/dy (y) ) dy/dx + (d/dx (x) ) y + d/dx (e²)

1/y dy/dx + eˣ + 0 = x (1) dy/dx + (1)y + 0

1/y dy/dx + eˣ = x dy/dx + y

1/y dy/dx - x dy/dx = y - eˣ

dy/dx (1/y - x) = y - eˣ

dy/dx = (y - eˣ) / (1/y - x)


Sub (2,1),

dy/dx = (1 - e²) / (1/1 - 2)

= (1 - e²) / -1

= e² - 1

Thanks for the answer

Welcome.