Question

Derivative of the √144-p

A) -p/√(144-p)
(B) √(144-p)/2p
(C) -1/2p√(144-p)
(D) -√(144-p)/2p

Answer 1

The derivative of √(144-p) with respect to p is -1/(2√(144-p)), which corresponds to option (C) in the question's choices.

Step-by-step explanation:

The student is asking for the derivative of the function √(144-p) with respect to p. When taking the derivative of a root function, we use the chain rule. The chain rule states that the derivative of a composed function is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

Let's take the derivative step-by-step:

1. 
   
3. Identify the outer function and the inner function. The outer function is the square root, and the inner function is (144-p).
4. 
   
6. Take the derivative of the outer function with respect to the inner function, which is 1/(2√(144-p)).
7. 
   
9. Take the derivative of the inner function with respect to p, which is -1.
10. 
    
12. Multiply these derivatives together to get the overall derivative.

The combined derivative is:

(1/(2√(144-p))) * (-1) = -1/(2√(144-p))

This matches option (C) from the provided choices.