Find the derivative y = (x ^ 2-5) ^ 3 + 2 (x ^ 2-5) ^ 2

Find the derivative y = (x ^ 2-5) ^ 3 + 2 (x ^ 2-5) ^ 2

y=(x²-5)³+2(x²-5)²
y'=[(x²-5)³]'+2[(x²-5)²]'
=3(x²-5)²×(x²-5)'+2×2(x²-5)'
=3(x²-5)²×2x+4×2x
=6x(x²-5)²+8x
=6x^5-60x³+158x

F (x) = - e ^ - x the derivation should be detailed

f(x)=-e^(-x)
f'(x)=-e^(-x)*(-1)
=e^(-x)

Y = x ^ x for y

Y = (e ^ LNX) ^ x = e ^ (xlnx), next you will

The sum of the first n terms of the sequence {an} is Sn = npan (n ∈ n *) and A1 ≠ A2. (1) find the value of the constant p; (2) prove that the sequence {an} is an arithmetic sequence

(1) When n = 1, A1 = PA1, if P = 1, a1 + A2 = 2pa2 = 2A2,  A1 = A2, it is contradictory to the known, so p ≠ 1. Then A1 = 0. When n = 2, a1 + A2 = 2pa2,  2p-1) A2 = 0.  A1 ≠ A2, so p = 12. (2) when Sn = 12nan, A1 = 0. N ≥ 2, an = sn-sn-1 = 12nan-12 (n-1)

The first workshop of carpet factory needs 5400 pieces of cement square bricks with a side length of 5 decimeters; how many pieces of cement square bricks with a side length of 8 decimeters?

About 2110 yuan

4 out of 15 + 5 out of 6

4 out of 15 + 5 out of 6
=8 out of 30 + 25 out of 30
=33 out of 30
=11 out of 10

(1 + √ 2) ^ n = xn + yn √ 2, where xn and yn are integers, find the limit of XN / yn when n tends to ∞

Consider the integer solution of Pell equation u ^ 2-2v ^ 2 = 1
The basic solution is u = 3, v = 2
So all the solutions of the equation can be expressed by UN + VN √ 2 = (3 + 2 √ 2) ^ n = (1 + √ 2) ^ (2n)
Obviously, when n tends to ∞, the limit of UN / VN given by this equation is obviously the same as that given by the equation
(1 + √ 2) ^ n = xn + yn √ 2 gives the same limit of XN / yn,
When n tends to ∞, the asymptotic equation u ^ 2-2v ^ 2 = 0 is taken as u ^ 2-2v ^ 2 = 1
U / v = √ 2
So LIM (xn / yn) = 2

In triangle ABC, if angle c equals 90 degrees, AC equals 12cm, BC equals 5cm, what is the height of hypotenuse AB?

Because the angle c is equal to 90 degrees, the triangle is a right triangle. First, use the Pythagorean theorem to calculate that the length of AB is the square of 12 under the root minus the square of 5 equals the height of 13 on the hypotenuse of the right triangle. The formula is that ab divided by C is AC multiplied by BC, and then divided by ab equal to 12 out of 13 multiplied by the height of 5 on the hypotenuse AB equals 60 out of 13. In fact, the Pythagorean theorem is very simple, Study hard, godfather

Let x ≥ 1, then the minimum value of the function y = (x + 2) (x + 3) x + 1 is______ ．

∵ y = (x + 2) (x + 3) x + 1 = (x + 1) + 2x + 1 + 3, ∵ x ≥ 1, ∵ x + 1 ≥ 2, and the double hook function y = x + 2x monotonically increases on [2, + ∞], ∵ when x = 1, the function y = (x + 2) (x + 3) x + 1 reaches the minimum, ∵ Ymin = 6

Integral 1. ∫ [(SiNx cosx) / (SiNx + cosx)] DX 2. ∫ DX / (X & # 178; - 7x + 12)

1. The original formula = - ∫ D (SiNx + cosx) / (SiNx + cosx)
=-ln|sinx+cosx|+C
2. The original formula = ∫ DX / (x-3) (x-4)
=∫[1/(x-4)-1/(x-3)]dx
=ln|x-4|-ln|x-3|+C