The geometric meaning of derivative is k slope. To find the tangent k slope of a function at x0 is to find the derivative of the function first, and then substitute the value of x0 into the derivative to get the tangent k slope at this point.

The difference and connection between derivative and K slope;

1, the origin is different: the origin of derivative is the rate of change of function value with the increase of independent variable, that is, the limit of △ y/△ x. K slope comes from microscopic analysis. For example, △y can be decomposed into the sum of A△x and o(Ox), and its linear principal part is called differential. When △x is small, the value of △y is mainly determined by the differential A△x, while o(Ox) has little influence on its size.

2. Different geometric meanings: the value of the derivative is the k slope of the tangent at this point, the value of the k slope is the increment of the ordinate along the tangent direction, and △y is the increment of the ordinate along the curve direction.

3. Connection: the derivative is a whole, and the slope of k is a point. For unary functions, differentiability must be oblique, and oblique must be differentiable.