Find the derivative of the following function using the limiting process.

Question

Quizplus · Accepted Answer

The process of taking the derivative using the limiting process involves taking the limit as h approaches 0 of [f(x+h) - f(x)]/h, where f(x) is the given function. Plugging in the given function to this formula, we get the following:

lim h→0 [(x+h)^5 - x^5]/h
= lim h→0 [x^5 + 5x^4h + 10x^3h^2 + 10x^2h^3 + 5xh^4 + h^5 - x^5]/h
= lim h→0 [5x^4 + 10x^3h + 10x^2h^2 + 5xh^3 + h^4]
= 5x^4

Therefore, the derivative of the given function is 5x^4, which corresponds to choice C.

Find the Derivative of the Following Function Using the Limiting