Original function: y=c(c is a constant), derivative: y' = 0；; Original function: y = x n, derivative: y' = NX (n-1); Original function: y=tanx, derivative: y' =1/cos2x; Original function: y=cotx, derivative: y' =-1/sin2x; Original function: y=sinx, derivative: y' = cosx Original function: y=cosx.

Derivative: y' =-sinx；; Original function: y = a x, derivative: y' = a xlna Original function: y = e x, derivative: y' = e x；; Original function: y=logax, derivative: y' = logae/x; Original function: y=lnx, derivative: y' =1/x.

Learning methods of mathematical derivatives in senior high school;

2. In general, let the derivative =0 and find the extreme point; Judging whether the sign of the derivative is positive or negative in the interval on both sides of the extreme point; If it is positive, the original function will increase, if it is negative, it will decrease, and then the image of the original function can be roughly drawn according to the increase and decrease. According to the image, you can find what you want, such as the maximum or minimum.

3. Under special circumstances, the sign of the derivative itself can be directly determined, that is, when the derivative is equal to 0 and there is no solution, it means that the original function is monotonous in the whole section. If the derivative is always greater than 0, it will increase; If the derivative is always less than 0, subtract it.