Let the function y = f (x) be determined by the equation sin y + e ^ x-xy ^ 2 = 0, and find D Y / D X

Let the function y = f (x) be determined by the equation sin y + e ^ x-xy ^ 2 = 0, and find D Y / D X

Fx=e^x-y^2
Fy=cosy-2xy
d y/d x=-Fx/Fy=(y^2-e^x)/(cosy-2xy)

Solution X-1 / 6 [12-6 (3 / 5x + 1)] = 3 / 7X-2
The equation of one variable is solved with test

Remove brackets
x-1/6(12-18/5x-6)=3/7x-2
x-2+3/5x+1=3/7x-2
transposition
x+3/5x-3/7x=-1
De denominator
35x+21x-15x=-35
33x=-35
∴x=-35/33
Test: when x = - 35 / 33, left =
Right =
Left = right
The root of the original equation is x = - 35 / 33

Is there a real number a such that the maximum value of the function y = sin ^ 2x + acosx + (5 / 8) a - (3 / 2) in the closed interval [0, π / 2] is 1? If so, find the corresponding value of A. if not, explain the reason

Derivation:
y（1）=2sinxcosx-asinx
Let the derivative be 0
We get (2sinx-a) cosx = 0
On the closed interval [0, Π / 2]
0

The difference between a number and its reciprocal is 7.875. What is the number?

8

If the point (2,3) is on the line y = 2x-1, then when x = 2, the solution of the quadratic equation x-2y = 2 is

If the point (2,3) is on the line y = 2x-1, then x = 2, y = 3
When x = 2, the solution of the quadratic equation x-2y = 2 is
2-2y=2
y=0
The solution of bivariate linear equation x-2y = 2 is x = 2, y = 0

What's the difference between the zero point theorem and Rolle's theorem of continuous function on closed interval

Rolle's theorem Let f (x) be continuous on the closed interval [abfjnb] (where a is not equal to b) and differentiable on the open interval (a, b), and f (a) = f (b), then there is at least one point ξ ∈ (a, b) such that f ｛ 39; (ξ) = 0zdh zero point theorem Let f (x) be continuous on the closed interval [a, b], and f (a) and f (b) have different signs (i.e. f (a) × f (b) & lt; 0), Then in the open interval (a, b), there is at least one zero point of the function f (x), that is, there is at least one point ξ (a ＆ lt; ξ ＆ lt; b) which makes f (ξ) = 095. How can V say the difference between Pt? If there are similarities, they are all the properties of continuous functions between closed intervals

If at least one solution of the quadratic equation MX & # 178; + MX + 4m + 12 = 0 with respect to X is less than 0, the value range of M is obtained

mx²+mx+4m+12=0
x=｛-m±√［m²-4m（4m+12）］｝/2m
= ［-m±√（-15m²-48m）］/2m
△=-15m²-48m
If there is a solution, it must be m < 0
Let [- M ± √ (- 15m & #178; - 48m)] / 2m < 0
∴ -m±√（-15m²-48m）＞0
±√（-15m²-48m）＞m
∵+√（-15m²-48m）＞0＞m
It must be - √ (- 15m & # 178; - 48m) > M
√（-15m²-48m）＜-m
-15m²-48m＜（-m）²
16m²+48m＞0
∵m≠0,
Two sides divided by M
16m+48＞0
m ＞-3
In conclusion, when - 3 ＜ m ＜ 0, at least one solution of MX & # 178; + MX + 4m + 12 = 0 is less than 0

Given that the image of the quadratic function y = MX & sup2; + 2m + m-4m & sup2; passes through the origin, the value of M, the symmetry axis and the opening direction of the quadratic function are obtained

If the formula is in the form of y = a (X-H) "+ K, the axis of symmetry, vertex coordinates and opening direction can be seen. Are you wrong? It should be y = MX" + 2x + m - 4m ", then y = m [x" + (2 / M) x] + m - 4m "= m [x" + 2 * (1 / M) x + (1 / M) "- (1 / M")] + m - 4m "= m [x + (1 / M)]" - 1 / M + m -

What is the value range of X that makes the formula √ X-2 meaningful

X-2 > = 0 means x > = 2

If - 2 is a root of the quadratic equation x + mx-8 = 0, find the other root

Let the other root be X
(-2)x=-8
x=4