Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.

2024年12月10日 · 当 x=y 时容易证明 f (\frac {1} {e},\frac {1} {e})=2\frac {1} {e}^ {\frac {1} {e}}>1 ，当 y=0 时有 f (x,0)=1 。 因此当 x\geq0,y\geq0 时有 f (x,y)=x^y+y^x\geq1

Graph of xy = yx. The line and curve intersect at (e, e). In general, exponentiation fails to be commutative. However, the equation has solutions, such as [1]

Solve your math problems using our free math solver with step-by-step solutions. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more.

taking LHS X+X'Y= (X+X') (X+Y) OR distributes over AND 1. (X+Y) (X+X'=1) X+Y=RHS 1 is identity for AND. Hence Proved. I don't think this is the proof that the asker is looking for: it doesn't use the algebraic properties of the operators. Also, I find your proof very hard to read.

It's just a convention, people decided that this y = f (x) means, the value of y at each value of the function f by changing x, in your case the name of the function is y, but you can call it whatever you want, f (x),y (x),t (x),z (x),cat (x),dog (x)... ecc. In your case you have called your function with the same graphical symbol of the result.

Official Release of PAST ELVN BY YX Please Follow Y.X On All Social Media Platforms: Instagram: https://www.instagram.com/y.x.official TikTok: https://www.tiktok.com/@y.x.official …

2024年12月16日 · Let u = 𝑦𝑥, v = 𝑥𝑦 & w = 𝑥^𝑥 Now, 𝒖 + 𝒗 + 𝒘 = 𝒂^𝒃 Differentiating 𝑤.𝑟.𝑡.𝑥 (𝑑 (𝑢 + 𝑣 + 𝑤))/𝑑𝑥 = (𝑑 (𝑎^𝑏))/𝑑𝑥 (𝑑 (𝑢))/𝑑𝑥 + (𝑑 (𝑣))/𝑑𝑥 + (𝑑 (𝑤))/𝑑𝑥 = 0 We will calculate derivative of u, v & w separately .

代回原方程，化为 g (D)*y=\varphi (x) 的形式，相当于是个非齐次线性方程，用特征方程随便解下就行了。 记得最后把t换成x。

I have it down to $$\ln (y)+ (x/y)y' = y'\ln (x)+y/x$$ The problem is factoring out $y'$, which leads to either $$y'=\frac {\ln (y)- (y/x)} {\ln (x)- (x/y)}$$ or to $$y'=\frac { (y/x)-\ln (y)} { (x/y)-\ln (x)}$$ ...