Find the derivative of the function using the definition of derivative. state the domain of the function and the domain of its derivative. f(t) = sqrt 9-x

The function f(x) is given by:

The domain of the function is the possible values of x where the function is defined.

We know that the square root function is defined when x≥0.

Hence, will be defined when

Hence, the domain of the function f(x) is:

Also, the definition of derivative of x is given by:

Hence, here by putting the value of the function we get:

Since,

Hence, we have:

Since, the domain of the derivative function is equal to the derivative of the square root function.

Also, the domain of the square root function is:

Hence, domain of the derivative function is:  

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