Proof of sum-difference of two functions, Mathematics

Assignment Help:

Proof of Sum/Difference of Two Functions : (f(x) + g(x))′  = f ′(x) +  g ′(x)

 It is easy adequate to prove by using the definition of the derivative.  We will start with the sum of two functions. Firstly plug the sum in the definition of the derivative and rewrite the numerator a bit.

(f(x) + g(x))' = limh→0 (f(x + h) + g(x + h) - (f(x) + g(x)))/h

= limh→0 (f(x + h) - f(x) + g(x + h) ­- g(x))/h

Then, break up the fraction in two pieces and recall the limit of a sum is the total of the limits. By using this fact we consider that we end-up with the definition of the derivative for all of the two functions.

(f(x) + g(x))' = limh→0 (f(x + h) - f(x))/h + limh→0 (g(x + h) - g(x))/h

= f'(x) + g'(x)

The proof of the difference of two functions in nearly the same therefore we'll provide this here without any clarification.

(f(x) + g(x))' = limh→0 (f(x + h) - g(x + h) - (f(x) - g(x)))/h

= limh→0 (f(x + h) - f(x) - (g(x + h) ­- g(x))/h

= limh→0 ((f(x + h) - f(x))/h) - ((g(x + h) ­- g(x))/h)

= f'(x) - g'(x)


Related Discussions:- Proof of sum-difference of two functions

Lpp, A paper mill produces two grades of paper viz., X and Y. Because of ra...

A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper i

How many dollars did they raise the first two days, The freshman class is p...

The freshman class is participating in a fundraiser. Their target is to raise $5,000. After the first two days of the fundraiser, they have raised 32 percent of their goal. How man

Example of set theory, Suggest me the solution: Consider the given unive...

Suggest me the solution: Consider the given universal set T and its subjects C, D and E T = {0, 2, 4, 6, 8, 10, 12} C = {4, 8,} D = {10, 2, 0} E = {0} Find out

???, a deposit of 10,000 was made to an account the year you were born afte...

a deposit of 10,000 was made to an account the year you were born after 12 years the account is worth 16,600 what is the simple interest rate did the account earn?

Square and square root., the value of square root of 200multiplied by squar...

the value of square root of 200multiplied by square root of 5=

Explain lobachevskian geometry and riemannian geometry, Explain Lobachevski...

Explain Lobachevskian Geometry and Riemannian Geometry ? Nineteenth century mathematician Nicolai Lobachevsky assumed that the summit angles of a Saccheri quadrilateral are ac

Find ad, A circle is inscribed in a triangle ABC having sides 8cm, 10cm and...

A circle is inscribed in a triangle ABC having sides 8cm, 10cm and 12cm as shown in the figure. Find AD, BE and CF.

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd