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The derivative and differential problems of college advanced numbers, please! !
① Set the chord equation: y=ax+b, and substitute two points (1, 4) and (3, 8) to get a=2.

That's right. y=x? The slope of the derivative of -2x+5 is: dy/dx=2x-2. Replace x=2 with a=dy/dx=2, and the points (2,5) of the parabolic equation are replaced.

From the slope 2, the tangent equation can be known through point (2,5): y=2x+ 1.

② Existence of partial derivative = existence of unilateral limit+limit value is equal to the value of this point.

When x= 1: f(x)=x? The limit of exists and equals to 1, but when x= 1, f(x)=2x? /3 takes the value of 2/3, so the second condition does not hold. Therefore, the right derivative does not exist, and similarly, the left derivative exists.

③ Step 1: Let z=dy/dx, then z = (dy/dt) ÷ (dx/dt) = t/(t+1).

Step 2: dz/dx = (dz/dt) ÷ (dx/dt) = [1/(1+t)? ] ? ( 1/et)

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