Find an equation of the tangent line to the curve (x^2)(e^y)+(ye^x)=4 at the point (2,0).

Question

I think you're supposed to use implicit differentiation.

Answer 1

The curve is , and the point is (2, 0).

We can use implicit differentiation to find y '.

The implicit(or total) derivation of is,

Substitute the values of (x, y ) = (2, 0) in the above equation.

.

This is the slope (m ) of the tangent line to the implicit curve at (2, 0).

To find the tangent line equation, substitute the values of and (x, y ) = (2,0) in the slope intercept form of an equation.

y = mx + b

.

Substitute and in y = mx + b.

.

The tangent line equation is .