The differential of y = 2 ^ (x ^ 2)

The differential of y = 2 ^ (x ^ 2)

y'=2^(x²)*ln2*(x²)'
=2x*2^(x²)*ln2

Find the general expression of the Nth derivative of the following functions
y=sin^2(x) y=xlnx y=1/(6+x-x^2)

1. Sin ^ 2 (x) can be changed into (1-cos2x) / 2 by half angle formula, and then (cos2x) ^ (n) = 2 ^ nxcos (2x + n π / 2) is brought into the above formula to get: [1-2 ^ nxcos (2x + n π / 2)] / 22. Y '= LNX + 1. We also know the n-order derivative formula of LNX, which is equivalent to finding the (n-1) order derivative of LNX. Just push back one bit, that is to replace n with n-1

1992 / 1993 numerator + last number, denominator - remove this number, the ratio is 2 / 3, find this number

(1992+x)/(1993-x)=2/3
2(1993-x)=3(1992+x)
x=(2*1993-3*1992)/5=-398

The general solution of derivative + 2XY = 2xe ^ - x2 of differential equation y
In the end, it's - x ^ 2. 2 won't be a corner mark. The title is - x ^ 2 power of 2xe

y'+2xy=2xe^(-x^2)
dy/(2xdx)+y=e^(-x^2)
dy/d(x^2)+y=e^(-x^2)
e^(-x^2)=u
-x^2=lnu
-dy/dlnu+y=u
-udy/du+y=u
ydu-udy=udu
y/u=v
dy=udv+vdu
uvdu-u*(udv+vdu)=udu
-u^2dv=udu
dv=-du/u
v=-lnu+C0
y/u=-lnu+C0
y=-ulnu+C0u
General solution y = x ^ 2E ^ (- x ^ 2) + c0e ^ (- x ^ 2)

If M & # 178; + 2Mn + 2n & # 178; - 6N + 9 = 0, find the value of M of N & # 178; part

If M & # 178; + 2Mn + 2n & # 178; - 6N + 9 = 0,
(m+n)²+(n-3)²=0
m=-n,n=3
Namely
m=-3,n=3
therefore
N and M
=- 3 out of 9
=-1 / 3

Xiaoma's calculation 56 - □ △ 8 is, first calculate the subtraction method, then calculate the division method, the result is 2, the correct result should be ()

56-40/8=51

How to find the distance from a point to a plane in space rectangular coordinate system?

Given cos θ = – 5 / 13, θ∈ (π, 3 π / 2), the value of COS (θ + π / 6) can be obtained

cosθ=–5/13
sinθ=–12/13
cos(θ+π/6)
=cosθ.cos(π/6)-sinθ.sin(π/6)
=(-5/13)(√3/2) + (12/13)(1/2)
= 6/13 -5√3/26

If AB is opposite to each other, it is indicated by sign

4 times log2 is the logarithm of bottom 3

4 ^ log2 is the logarithm of base 3
=2 ^ 2log2 is the logarithm of base 3
=2 ^ log2 is the logarithm of the base 3
=3²
=9