For the function y=f(x), its slope can be expressed as follows: assuming that the function y=ax+b, its slope is a. If the function is a quadratic function y = ax 2+bx+c, its slope is b. If the function is a cubic function y = ax 3+bx 2+CX+d, its slope is b.

If the function is a power function y = x n, its slope is n; if the function is a logarithmic function y=log_ax, its slope is 1/x; if the function is a trigonometric function y=sinx or y=cosx, its slope is cosx or -sinx.

If the function is an inverse trigonometric function y=arcsinx or y=arccosx, then its slope is1√ (1-x 2) or-1√ (1-x 2). If the function is a hyperbolic sine function y=sinhx, then its slope is coshx. If the function is hyperbolic cosine function y=coshx, then its slope is sinhx. If the function is a natural logarithmic function y=lnx, then its slope is1/x.

curriculum standards

In the compulsory education stage, students learn the function once, and its geometric meaning is represented by a straight line. The coefficient of the first term is the slope of the straight line, but it cannot be expressed when the straight line is perpendicular to the X axis. Although the term slope is not clearly given, in fact, the idea has penetrated into it.

In senior high school, compulsory one and compulsory two discussed the problem of straight line, and elective one and elective two also mentioned some problems related to straight line. The contents listed above actually involve the concept of slope, so it can be said that the concept of slope is one of the important mathematical concepts that students gradually accumulate.