Derivative plays an important role in mathematics. First of all, derivative is one of the basic concepts of calculus, which describes the tangent slope of a function at a certain point and reflects the rate of change of the function at that point. Through derivation, we can study the monotonicity, extreme value and concavity of the function, so as to better understand and analyze the behavior of the function.

Secondly, derivatives also play an important role in solving practical problems. For example, in physics, concepts such as speed and acceleration can be expressed by derivatives; In economics, economic indicators such as marginal cost and marginal income can also be calculated by derivatives. In addition, derivatives are also widely used in biology, engineering, computer science and other fields.

Furthermore, derivative and integral are two basic operations of calculus, and they are closely related. Derivative can be regarded as the "inverse operation" of integral, and integral can be regarded as the "accumulation" of derivative. Through this mutual transformation, we can solve all kinds of complicated problems more conveniently.

Finally, derivative also plays a key role in the development of mathematical theory. For example, Newton and Leibniz established the basic theoretical framework of calculus by studying the properties of derivatives and integrals. In addition, derivatives are closely related to many other mathematical concepts and theorems, such as Taylor series, Lobida rule, Lagrange multiplier method and so on.

In a word, the importance of derivative in mathematics is self-evident. It is not only the foundation of calculus, but also an important tool to solve practical problems and has a far-reaching impact on the development of mathematical theory.