Calculate the derivative f'(x) first, and the essence of the derivative is the slope of the curve. For example, there is a point (a.b) on the function, and the derivative f'(a)=c at this point, then the tangent slope at this point (a.b) is k=c, assuming that the tangent equation is y=mx+n, then m=k=c, AC+n..

Formula: Take the obtained derivative value as the slope k, use the origin (x0, y0), and the tangent equation is (y-b)=k(x-a).

Extended data:

Tangent equation is a slope equation to study tangents and tangents, involving geometry, algebra, physical vectors, quantum mechanics and so on. It is about the study of the tangent coordinate vector relationship of geometric figures. Analysis methods include vector method and analytical method.

Vector method

Let a point on the circle be a, then what is the vector between that point and the center o? Because the tangent through this point is perpendicular to the radius in this direction, the dot product of the unit vector and the vector OA in the tangent direction is 0.

Let any point b on a straight line be (x, y), then for the vector in the direction of the straight line,? This is the dot product of vectors AB and OA.

So there is?

oblong

If the equation of the ellipse is point p.

On an ellipse, the tangent equation of the ellipse passing through point P is

It is proved that if the ellipse is and the tangent point is, then ... (1)

Derive ellipse, that is, tangent slope,

So the tangent equation is (1), and the tangent equation is simplified. .

hyperbola

If the equation of hyperbola is point P.

On hyperbola, the method of proving the tangent equation of hyperbola passing through point P is similar to that of ellipse.

References:

Baidu Encyclopedia-Tangent Equation