I want to find the second derivative of F (x, y) = siny + e ^ x-xy-1 in detail

I want to find the second derivative of F (x, y) = siny + e ^ x-xy-1 in detail

∂z/∂x=e^x-y∂z/∂y= cosy-x=>∂²z/∂x²=e^x ∂²z/∂y²= -sinx∂²z/∂x∂y= -1∂²z/∂y∂x=-1

f(X)=(X+100)(X+99)… (X+1)X(X-1)… (X-100), find the derivative of F (0)
Please talk about each step carefully! Thank you

You see, f '(x) = x' [(x + 100) (x + 99) (x+1)(x-1)…… (x-100)]+x[(x+100)（x+99)…… (x+1)(x-1)…… (X-100)] 'this is the derivative algorithm. Do you have the formula in the book (high school elective 2-2) that is to put forward X and regard the others as a whole

Given that f (x) = (x-1) (X-2) (x-3). (X-100), find the derivative of F (99)

F (99) should be a constant value and the derivative is 0. It should be the derivative of F '(99)
Solution: the nth factor in F (x) is (x-n)
According to f (x) * g (x) *The derivation theorem of H (g) shows that:
In the derivative of F (x), except for the derivation of (x-99), all the other derivations contain the terms of (x-99). Therefore, when x = 99, the values of these terms are all 0
So the value is: F '(99) = 98 * 97 * 96 *1*（-1）
＝-98!