The normal vector problem of conic How to express the normal vector at the point P (x0, Y0, Z0) of the conic f (x, y, z) = 0 in three-dimensional space?

The normal vector problem of conic How to express the normal vector at the point P (x0, Y0, Z0) of the conic f (x, y, z) = 0 in three-dimensional space?

The direction is (FX (x0, Y0, Z0), FY (x0, Y0, Z0), FZ (x0, Y0, Z0))
The value of partial derivative of meaning curve of FX (x0, Y0, Z0) to X at point P

Can calculus product from 0 to 0!

Only when the function is defined when x = 0, can the product be from 0 to 0. But the result must be 0

In calculus, derivative is used to define the derivation of quotient rule in textbooks. I would like to ask, on the basis of known product rule, can product rule be used to derive quotient rule?
For example, to find the derivative of a fraction like f / g, I use the product rule to derive (f'g-f) / G ^ 2 instead of (f'g-fg ') / G ^ 2. Which step is wrong?
(f/g)'=(f*g^-1)=f'g^-1+f(g^-1)'=f'^-1-fg^-2=g^-2(f'g-f)=(f'g-f)/g^2

f'^-1-fg^-2-->(f'^-1-f(g^-2)*g')
And another G '
G is also a function, which requires derivation

The sum of 4 times of a number and 5.5 times of it is 1.9. What is the number?

1.9 △ 4 + 5.5, = 1.9 △ 9.5, = 0.2. A: this number is 0.2

12 × 52 of 99 and 13 is calculated by a simple method

12 × 52 of 99 and 13
=（100-1/13）×52
=100×52-1/13 ×52
=5200-4
=5196

Factorization of a ^ 2x ^ 2 + 3ax-35
Is (a ^ 2) * (x ^ 2) + 3ax-35 factorization

a^2x^2+3ax-35 =0
ax=(-3±√149)/2
a^2x^2+3ax-35
=[ax-(-3+√149)/2)][ax-(-3-√149)/2)]

(minus 2 / 5) plus (minus 3 and 4 / 7) minus 1.6 minus (minus 11 / 7)
Request process! Know the teaching, good must add reward! To detailed Oh!

-2/5-25/7-8/5+11/7=-4

If you reduce the length of a cuboid by 5cm, it will become a cube. The surface area of the cube is 60cm less than that of the cuboid?

What do you want?
The circumference of a face of a cube is 60 △ 5 = 12
So the edge length is 12 △ 4 = 3
So it turns out that the bottom of the cuboid is a square with a side length of 3 and a height of 3 + 5 = 8
Surface area 2 × (3 × 3 + 3 × 8 + 3 × 8) = 114 square centimeters
Volume 3 × 3 × 8 = 72 CC

128 times 126 / 127

127 times 126 / 127 plus 126 / 127 equals 126 and 126 / 127

In 1-1000, how many numbers are not divisible by 2, 3 or 5?

Divisible by 2: 500
Divisible by 3: 333
Divisible by 5: 200
Again by 2 again by 3:1000 / 6 = 133
Again by 3 again by 5:1000 / 15 = 66
By 2 and by 5:1000 / 10 = 100
Number = 1000-500-333-200 + 133 + 66 + 100 = 266