1, high school mathematics derivative formula: (C)'=0, and c is a constant; (x n)' = NX (n-1), where n is a constant and n ≠ 0; (sinx)' = cosx； (cosx)' =-sinx； (tanx)'=sec^2x； (cotx)'=-csc^2x； (a x)' = a xlna, a > 0 and a ≠1; (e^x)'=e^x； (logax)'=logae/x, a > 0 and a≠ 1.
2. Derivation is widely used in mathematics and physics. In mathematics, derivation can help us to study the properties of functions, such as monotonicity and extremum. The derivative function of the function can be obtained by derivation, and then the increase and decrease of the function can be analyzed, which provides a powerful tool for solving some mathematical problems.
3. Derivation also plays an important role in physics. For example, when studying the law of motion of an object, we can get the expressions of velocity and acceleration by derivation. These expressions can help us understand the motion state of objects, such as the direction of speed and the magnitude of acceleration. In addition, derivation is also a common tool in the fields of thermodynamics and electromagnetism.
The origin of derivation
The origin of derivation can be traced back to17th century. Scientists began to study the shapes of curves and surfaces and tried to find mathematical models to describe these shapes. They found that the tangent slope of the curve can be obtained by derivative, and then the changing trend of the curve can be described. Therefore, derivation has become an important tool to study the shape of curves and surfaces.
2. In calculus, derivative is one of the foundations of calculus. Calculus is a science that studies the rate of change of functions, and derivation is to find the rate of change of functions through mathematical operations. Through derivation, we can get the derivative of the function, and then analyze the properties of the function, such as increase and decrease, extreme value and so on. Therefore, derivative plays a vital role in calculus.
3. Derivation is not only widely used in mathematics, but also plays an important role in other disciplines. For example, in physics, the acceleration and velocity of an object can be obtained by derivation; In economics, derivation can analyze the changing trend of economic variables such as cost function and income function.