Y ^ 2 + x = x ^ 3-y + 6, what is his second derivative It's best to take steps, pay attention to 2 times

Y ^ 2 + x = x ^ 3-y + 6, what is his second derivative It's best to take steps, pay attention to 2 times

Derivation of X
2y*y'+1=3x^2-y'
(2y+1)y'=3x^2-1
y'=(3x^2-1)/(2y+1)

Sum L + 2x + 3x2 + +nxn-1.

When x = 1, the result is easy to calculate. The following calculations are based on the premise that x ≠ 1
Method 1: remember that the result of the original formula is s, and then multiply the left and right by X at the same time, and the result can be calculated by subtracting the two formulas
Method 2: use the equation
1+x+x^2+…… +x^n=[1-x^(n+1)]/(1-x)
If both sides take derivatives of X at the same time, we can wait for the result
S=[1-(n+1)x^n+nx^(n+1)]/(1-x)^2

How to derive 1 / (2x)
Step by step

1 / 2 is a coefficient constant, so what we really need is the derivative of 1 / X. 1 / x = the - 1 power of X. The derivative of the n-th power of X is the (n-1) power of n * X
The derivative of 1 / X is - 1 * 1 / X & sup2;
The derivative of 1 / (2x) is - 1 / (2x & sup2;)

2X + 1 derivation, process
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(2x + 1)' = 2*x' + 1'
= 2*1 + 0
= 2
(2x)' = 2*x'
= 2*1
= 2