Question

Find the derivative of the function f(x)=ln(eˣ+18).

Answer 1

To find the derivative of the function f(x) = ln(eˣ+18), use the chain rule. The derivative of f(x) is eˣ / (eˣ+18).

Step-by-step explanation:

To find the derivative of the function f(x) = ln(eˣ+18), we can use the chain rule. Let u = eˣ+18. The derivative of u with respect to x is du/dx = eˣ. Then, the derivative of f(x) = ln(u) with respect to x is given by df(x)/dx = (1/u) * du/dx = (1/(eˣ+18)) * eˣ. Therefore, the derivative of f(x) is df(x)/dx = eˣ / (eˣ+18).