Answer:
a) G'(t) = -11/(5+t)²
b) Domain of the function
(-∞ < t < -5) and (-5 < t < ∞)
c) Domain of the derivative too
(-∞ < t < -5) and (-5 < t < ∞)
Step-by-step explanation:
a) Obtaining the derivative of the function from the definition of a derivative is presented in the attached image to the question.
b) Domain of the function includes every value of t for which the function exists.
The function only ceases to exist when the function goes to ±∞.
And this occurs when the denominator = 0
The function does not exist at (5 + t) = 0; t = -5.
So, the function exists in every domain of real numbers except at t = - 5
Hence, the domain of the function is (-∞ < t < -5) and (-5 < t < ∞)
c) Domain of the derivative
This is similar to the domain of the function.
The derivative ceases to exist only when
(5+t)² = 0; t = - 5
Hence, the domain of the derivative too is (-∞ < t < -5) and (-5 < t < ∞)
