How to prove that the derivative of a pair of inverse functions is reciprocal

How to prove that the derivative of a pair of inverse functions is reciprocal

y = f(x)
G is the inverse function of F
If Y1 = f (x1), y2 = f (x2)
Then X1 = g (Y1), X2 = g (Y2)
According to the definition of derivative, G '= g (Y1) - G (Y2) / y1-y2 = x1-x2 / F (x1) - f (x2) = 1 / F

How to understand gradients and directional derivatives in big one high numbers There are some concepts in my textbook, but I want to have a deeper understanding. The best image is to think and understand from many angles

If the roof is a curved surface, the ground you are on is the domain of definition. If you stand at a point, your head corresponds to a point on the roof. When you want to leave from this point, the height of the roof will increase or decrease, and the change will be

The first high number uses derivative definition to find limit, and fixed weight thanks Given the existence of the function f '(x0), then the limit of [f (x0 - △ x) - f (x0)] / △ x when △ X - > 0, and the limit of F (x0 + H) - f (x0-h) / h when h → 0

Let H = - △ x, when △ x → 0, there is h → 0 ﹤ Lim [f (X. - △ x) - f (X.)] / △ x △ x → 0 = Lim [f (X. + H) - f (X.)] / (- H) H → 0 = - Lim [f (X. + H) - f (X.)] / HH → 0 = - f '(X.) Lim [f (X. + H) - f (X. - H)] / HH → 0 = Lim [f (X. + H) - f (X.) +

Water flows out of a hemispherical flume with a radius of 13 m and the flow rate is 0.6 m3 / s. what is the change rate of water level when the water depth is 8 m? What is the change rate of the radius of the water surface? PS: that's the original question... No picture

Let y be the volume of water, h the water level, r the radius of the ball, r the radius of the water surface, V the velocity and t the time
If h takes the derivative of time, H '(T) is obtained. If r takes the derivative of time, R' (T) is obtained
y=(2πR^3)/3-vt ①
Y = π H ^ 2 (R-H / 3) 2
R = √ [R ^ 2 - (R-H) ^ 2] 3
There is (2 π R ^ 3) / 3-vt = π H ^ 2 (R-H / 3), and there is - v = 2 π rHH '(T)
H '(T) = - 0.0009187 M / s
From (3) R ^ 2 = R ^ 2 - (R-H) ^ 2, the two sides of the time derivative, 2rr '(T) = 2RH' (T) - 2H '(T)
However, r = 12m is obtained from ③ and substituted into the data
r'(t)=-0.0003827 m/s

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The plane rectangular coordinate system should contain these two
Algebra is called function
Geometric is called analytic geometry
It should come out

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(1) If 3x + y = 1 + 3M (2) x + 3Y = 1-m (1) + (2), 4x + 4Y = 2 + 2m, 4 (x + y) = 2 (1 + m), x + y = (1 + m) / 2, and if x + Y > 0, then (1 + m) / 2 > 0, then M > - 1. Let AC intersect BD at point E, then AE = 3 * sin45 degree = (3 radical 2) / 2 be = 7 * * sin45 degree = (7 root sign 2) / 2 then AB = root sign (AE square + be flat)

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A ^ 4 + B ^ 4 + C ^ 4 + D ^ 4 = 4abcd is a ^ 4 + B ^ 4 + C ^ 4 + D ^ 4 + D ^ 2 ^ 2 + C ^ 4 + D ^ 4-2c ^ 2 ^ 2 ^ 2 = 4 abcd-2a ^ 2 ^ 2 ^ 2-2c ^ 2 ^ 2 ^ 2 is (a ^ 2-B ^ 2) ^ 2 + (C ^ 2-D ^ 2) ^ 2 = - 2 (ab-cd) ^ 2 there are three complete square numbers. Obviously, a ^ 2 = B ^ 2 = D ^ 2 = D ^ 2Ab ^ 2Ab = CD, so a = B = C = D, so the four sides are equal, so a = b = C = D, so the four sides are equal, so a = b = C = D, so the four sides are equal, so the four sides are equal, so a = b = C quadrilateral

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