show [f(xop), d/dx] = -df/dx

please help, can sb gives a hint? I really appreciate.

To simplify the given expression, we need to apply the chain rule in calculus. The chain rule states that if we have a function g(x) = f(h(x)), then the derivative of g(x) with respect to x is given by:

d/dx(g(x)) = d/dx(f(h(x))) = f'(h(x)) * h'(x)

Now, let's apply this rule to the expression [f(xo∂p), d/dx]. The notation [f(xo∂p), d/dx] represents the derivative of f(xo∂p) with respect to x.

So let's break it down step by step:

1. Identify the inner function that will be denoted by h(x). In this case, h(x) = xo∂p.

2. Identify the outer function denoted by f. In this case, f(x) is the outer function.

3. Calculate the derivative of the outer function f(x) with respect to its argument. This derivative is given as df/dx.

4. Calculate the derivative of the inner function h(x) with respect to its argument. This derivative is given as d/dx(xo∂p).

5. Multiply the derivative of the outer function (df/dx) with the derivative of the inner function (d/dx(xo∂p)).

Since the problem asks us to find [f(xo∂p), d/dx], we can simplify the expression as:

[f(xo∂p), d/dx] = df/dx * d/dx(xo∂p)

Therefore, the simplified expression is [-df/dx * d/dx(xo∂p)].

Please note that in order to evaluate the derivative d/dx(xo∂p), we need to know the specific function xo∂p. You will need to provide more details or context in order to obtain the exact result.