What is the method of finding tangent equations by derivatives?

Find the tangent equation at a point.

This is represented in the equation.

The x brought into this point is the slope in the derivative, and the y is the slope.

And find the tangent equation at a certain point.

I don't know if it's in the equation.

Therefore, it cannot be found with a derivative function (I think this needs to be analyzed on a case-by-case basis, which is generally conditional in the title).

Anyway, you keep in mind that the y of the derivative represents the slope (x is the x of the tangent point).

The derivative is used to find the tangent equation of the curve, which is also to find the derivative first, and then calculate the y value of the derivative, which is the slope of the tangent, combine the tangent point and the slope together, and find the tangent equation according to the point slope.

Finding the tangent equation of the curve is one of the important applications of the derivative, and the key to finding the tangent equation with the derivative is to find the tangent point p(o) and the slope, and the method is: let p(o,o) be a point on the curve y=f(x), then the tangent equation of the tangent point of p is: y-%=f'（x）x-）.

If the curve y=f() is defined by the tangent of the point p(xf() when the tangent of the point p(xf() is parallel to the y-axis (i.e., the derivative does not exist), the tangent equation is x=x·

Finding tangent equations is relatively easy content, and it is best not to make mistakes in this type of problem, it is a pity to lose points. If you want to find the extreme value, the most value, and need to be classified and discussed, you can find the derivative, and then find the zero point of the derivative, and then answer the question according to the actual situation.

DerivativesTangent equationsThe method is as follows:

1. First, find the derivative value of the function at the point (x0, y0), which is the slope value of the tangent of the function at the point of x0. After substituting the point coordinates (x0, y0), the tangent equation can be obtained by using the point oblique formula.

2. When the derivative value is 0, the tangent of the change point is y=y0; When the derivative does not exist, the tangent is x=x0; When it is not derivable at that point, there is no tangent.

3. If a certain point touches the nucleus on the curve, let the curve equation be y=f(x), and a point on the curve is the first excavation (a, f(a)). Find the derivative of the curve equation and get f'(x), substituting a point to get f'(a), which is the tangent slope of the crossing point (a, f(a)), is obtained from the point oblique equation of the straight line. y-f(a)=f'(a)(x-a)。

The basic derivative is as follows:

1. Linearity of derivative: Derivative of the linear combination of functions is equivalent to first deriving each part of the argument and then taking the linear combination.

2. The derivative of the product of two functions.

One lead times two + one by two leads.

3. The derivative of the quotient of two functions is also a fraction.

Child-led mother-child-by-child) divided by the female squared.

4. If there is a composite function.

then use the chain rule. Derivation.

The formula for the four rules of operation of derivatives: (u+v).'=u'+v'；(u-v)'=u'-v'；(uv)'=u'v+uv'；(u/v)'=u'v-uv')/v^2。Derivatives are local properties of functions.

The derivative of a function at a certain point describes the rate of change of the function around that point. If the arguments and values of a function are real, the derivative of the function at a point is the tangent slope of the curve represented by the function at that point. The essence of the derivative is to approximate the function linearly through the concept of limit.

The derivative is used to find the tangent equation of the curve, which is also to find the derivative first, and then calculate the y value of the derivative, which is the slope of the tangent line.

Finding the tangent equation of the curve is one of the important applications of the derivative, and the key to finding the tangent equation with the derivative is to find the tangent point p(o) and the slope, and the method is: let p(o,o) be a point on the curve y=f(x), then the tangent equation of the tangent point of p is: y-%=f'（x）x-）.

If the curve y=f() is defined by the tangent of the point p(xf() when the tangent of the point p(xf() is parallel to the y-axis (i.e., the derivative does not exist), the tangent equation is x=x·

Finding tangent equations is relatively simple content, and it is best not to make mistakes in this type of problem, and it is a pity to lose points. If you want to find the extreme value, the most value, and need to be classified and discussed, you can find the derivative, and then find the zero point of the derivative, and then bury the root to answer the question according to the actual situation.

The step of finding the tangent equation of a function image with a fixed point is as follows:

1) Set the tangent point to (x0,y0);

2) Find the derivative of the original function, and substitute x0 into the derivative function to obtain the slope k of the tangent;

3) Write the tangent equation from the slope k and the tangent point (x0, y0) with the point oblique equation of the straight line;

4) Substituting the fixed-point coordinates into the tangent excavation equation to obtain equation 1, and substituting the tangent points (x0, y0) into the original equation.

The tangent equation formula for derivatives is as follows: the derived value is used as the slope k and then the original point (x0, y0) is used, and the tangent equation is (y-b)=k(x-a).

Method for finding tangent equations for derivatives.

Calculate the derivative f first'(x), the essence of the derivative is the slope of the curve, for example, there is a point ( on the function, and the derivative f of that point'(a)=c then the tangent slope of the point k=c, assuming that this tangent equation is y=mx+n, then brother burns m=k=c, and ac+n=b, so y=cx+b-ac

Formula: The derived value is used as the slope k and then the original point (x0, y0) is used, and the tangent equation is (y-b)=k(x-a).

The algorithm of derivatives

Subtraction law: envy type virtual (f(x)-g(x)).'f'(x)-g'(x)

Addition rule: (f(x)+g(x)).'f'(x)+g'(x)

Multiplication rent model: (f(x)g(x))).'f'(x)g(x)+f(x)g'(x)

Division rule: (g(x) f(x))).'g'(x)f(x)-f'(x)g(x))/f(x))^2

Find the derivative of the function at (x0, y0).

The derivative value is the value of the slope of the tangent of the function at x0. After substituting the coordinates of the point (x0, y0), the tangent equation can be obtained by guessing the branch point trillion bucket oblique formula.

When the derivative value is 0, the tangent of the change point is y=y0

When the derivative does not exist, the tangent is x=x0;

When it is not derivable at that point, there is no tangent.