find the derivative using limit definition
in Calculus Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

Derivative of (x²-4)(x²-5) from first principles.

Let y=f(x).

We consider a small increment h in x which creates a corresponding increase k in y.

y+k=((x+h)²-4)((x+h)²-5).

y+k=(x²+2xh-4)(x²+2xh-5). h² is ignored as insignificantly small.

y+k=x⁴+4x³h-9x²-18xh+20.

To find k, we subtract f(x):

k=x⁴+4x³h-9x²-18xh+20-(x⁴-9x²+20).

k=4x³h-18xh.

k/h=4x³-18x.

In the limit as h,k→0, h/k=dy/dx=4x³-18x. This is the derivative of f(x).

by Top Rated User (804k points)

Related questions

Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
85,844 questions
91,599 answers
2,225 comments
15,901 users