Question

Differentiate. (Assume k is a constant.). . y = 1 / (p + ke^p). . I tried using the quotient rule.... (f/g)' = (gf' - fg') / g^2. . and ended up with . (1-pke^(p-1)) / (p+ke^p)^2. . which is apparently wrong.

Answer 1

To differentiate the function y = 1 / (p + ke^p), you can use the quotient rule. The quotient rule states that if you have a function f(x) divided by g(x), the derivative is given by (g(x)f'(x) - f(x)g'(x)) / g(x)^2. Applying the quotient rule to the function y = 1 / (p + ke^p), we have f(x) = 1 and g(x) = (p + ke^p). Now, we can find the derivatives and plugging these values into the quotient rule gives us the derivative of the function.

Step-by-step explanation:

To differentiate the function y = 1 / (p + ke^p), you can use the quotient rule. The quotient rule states that if you have a function f(x) divided by g(x), the derivative is given by (g(x)f'(x) - f(x)g'(x)) / g(x)^2.

Applying the quotient rule to the function y = 1 / (p + ke^p), we have:

• f(x) = 1
• g(x) = (p + ke^p)

Now, we can find the derivatives:

• f'(x) = 0 (since the derivative of a constant is zero)
• g'(x) = 1 + k(e^p)(dp/dx)

Plugging these values into the quotient rule, we get:

(1)(1 + k(e^p)(dp/dx)) - (0)((p + ke^p)) / (p + ke^p)^2

Simplifying this expression gives us the derivative of the function.