How many times is the root x? How many times is one of X to the power of X? Y = 3x, then y '=? (derivative) tangent equation with the 5th power slope of curve y = x of 5? Can the last two questions be explained clearly? And the one who answers all the questions correctly is the last one. What's the use of knowing that the answer won't do?

How many times is the root x? How many times is one of X to the power of X? Y = 3x, then y '=? (derivative) tangent equation with the 5th power slope of curve y = x of 5? Can the last two questions be explained clearly? And the one who answers all the questions correctly is the last one. What's the use of knowing that the answer won't do?

1 / 2, - 1, y '= 3, y' = 5x ^ 4, let y '= 5 get x = + - 1, the tangent point is (1,1) or (- 1, - 1), and the tangent equation is y = 5x-4 or y = 5x + 4

Let the function f (x) = e ^ X-X. let the solution set of inequality f (x) > ax be p and {x | 0

That is to say, e ^ x-x > ax is constant on [0,2], because when x = 0, it is obvious that e ^ x-x > ax is constant on (0,2), so e ^ X / X-1 > A is constant on (0,2), so g (x) = e ^ X / X - 1, so the minimum value of G (x) > Ag '(x) = (e ^ x * x-e ^ x) / X ²= e^x(x-1)/x ² 00g(x)...

A derivative calculation, Y equals V times the square of u, V equals x plus 2A. U equals x minus A. I know how to divide them into several functions. How to calculate it?

What about the problem? Y = (x + 2a) (x-a) ^ 2V = x + 2A u = x-a z = U2, so the reduction below Y's derivative = v'u ^ 2 + V (u ^ 2) '= 1 (x-a) ^ 2 + (x + 2a) 2 (x-a) 1 depends on yourself. If you can skillfully master the derivative formula and the derivatives of several elementary functions, you can see at a glance that the key to this problem is (x -

Ask for a derivative problem in high school mathematics For any x belonging to R, the derivative of function f (x) exists. If f '(x) > F (x) and a > 0, the following correct is () A f(a)＞e^a * f(0) B f(a)＜e^a * f(0) C f(a)＜f(0) D f(a)＞f(0)

A
When f '(x) = f (x), f (x) = e ^ x

Make an internal trapezoid in the semicircle with radius r, so that its bottom is diameter, and the other three sides are circular strings, then when the area of the trapezoid is the largest, the length of the upper bottom of the trapezoid is __

Let the upper bottom of the trapezoid be 2x in length, h in height, and s in area, ∵ H = R2 − X2, ∵ s = (R + x) •    R2 − X2, S / = (R − 2x) (R + x) R2 − x2 let s' = 0, get x = R2 (x = - R), then H = 32R. When x ∈ (0, R2), s' > 0; When R2 < x < R, s ′ < 0. When x = R2, s

On the image of function y = x3-8x, the inclination angle of its tangent is less than π 4, the number of points whose coordinates are integers is () A. 3 B. 2 C. 1 D. 0

∵ tangent inclination angle is less than π
4，
‡ slope 0 ≤ K ＜ 1
If the tangent point is (x0, x03-8x0), then k = y ′| x = x0 = 3x02-8,
∴0≤3x20-8＜1，8
3≤x02＜3．
∵ x0 ∈ Z, ∵ x0 does not exist
So choose D