To find the derivative of the function f(c) = a^c + x - 4c with respect to c, we can use the rules of differentiation.

The derivative of a constant (x in this case) is zero, so it does not contribute to the derivative of the function.

The derivative of a^c with respect to c is ln(a) * a^c.

The derivative of 4c with respect to c is simply 4.

Therefore, the derivative of the function f(c) = a^c + x - 4c with respect to c is:

f'(c) = ln(a) * a^c - 4

or equivalently,

f'(c) = ln(a^c) * a - 4

where ln denotes the natural logarithm.
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