How to find the derivative of functions: y=(5x+7)(x+5)^3
Mathematics · College · Tue Nov 03 2020
Answered on
Given the function:
y = (5x + 7)(x + 5)^3
Find the derivative.
Solution:
Since we are given two functions to be derived we can use the chain rule formula and product rule.
Chain Rule:
f'(x) = f(g(x)) . g'(x)
Product Rule:
f(x).g(x) = f'(x)g(x) + f(x) g'(x)
y= (5x + 7)(x + 5)^3
y' = 5 (x + 5)^3 + 3(x+5)^2 (1) (5x + 7)
y' = (5x + 25)^3 + 3(x +5)^2 (5x + 7)
Final answer:
y' = (5x + 25)^3 + 3(x +5)^2 (5x + 7)