If this is how your post should have read, then calculating the derivative of

will give you the slope of the tangent.

The slope of the line

is

The normal and the tangent are perpendicular, so you can find what the tangent slope needs to be.

The derivative being equal to this tangent slope will obtain the x co-ordinate of

The y co-ordinate is obtained by placing the x co-ordinate into f(x).

Finally, to get the equation of the tangent, use the equation of the line formula,

using the slope calculated and the co-ordinates of