Open study

is now brainly

With Brainly you can:

  • Get homework help from millions of students and moderators
  • Learn how to solve problems with step-by-step explanations
  • Share your knowledge and earn points by helping other students
  • Learn anywhere, anytime with the Brainly app!

A community for students.

Problem : Find the derivatives of the function using the limit of definition y=x^4

Calculus1
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Join Brainly to access

this expert answer

SIGN UP FOR FREE
still the same type of question? try going http://www.math.hmc.edu/calculus/tutorials/limit_definition/ they show you examples. just apply your question to how they solve it.
It cant be that you were taught 2 other similar questions but still cant solve it.
im confused about the exponent 4

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

do you know how to do (a+b)^4?
no
its the binomial theorem or pascal triangle
1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 etc....
for example just look at the pascal triangle for the coefficients (a+b)^2= 1a^2 + 2ab +1b^2= a^2 +2ab+b^2 can you guess whats (a+b)^3? and for (a+b)^4?
note it can be like (x+y)^3 ? or (x+y)^4 ?
so power of 3 we get the coefficients of 1 3 3 1 therefore the answer for (x+y)^3= x^3 +3x^2y +3 xy^2 + y^3 can you guess for (x+y)^4 ?
the reason i want you to learn this is when you go solved for the derivative of y=x^4 you will get to find (x+y)^4
tnx a lot . i need to study more about this
im here now to teach you the easier way of doing it
ok for the power of 4 the coefficents inthe pascal triangle are 1 4 6 4 1 therefore (a+b)^4 = a^4 + 4a^3 b +6 a^2 b^2 +4 a b^3 + b^4 or (x+y)^4= x^4 +4x^3 y + 6 x^2 y^2 + 4x y^3 + y^4 did you see it ?
yes
now for practice y=x^2 \[y+\Delta y=x +\Delta x\] \[\Delta y=x+\Delta x - y\] \[\Delta y= (x+\Delta x)^{2}-x ^{2}\]
can you try solving that first ?
wait
i try solving it
the answer is 2x
\[\Delta y=f(x+\Delta x) - y\] \[\Delta y=(x+\Delta x)^{2}- x ^{2}\] \[\Delta y= x ^{2 }+ 2x \Delta x +\Delta x ^{2} -x ^{2}\] add or subtract we get \[\Delta y= 2x \Delta x+\Delta x ^{2}\] now the derivative is \[y'=f'(x)= \lim _{\Delta x ->0}\frac{ \Delta y }{ \Delta x }=\] \[= \lim _{\Delta x->0}(\frac{ 2x \Delta x+\Delta x ^{2} }{ \Delta x })\] try to cancell something in there
i know it already the answer is 2x
ok good can you try it if its y=x^4 ? do the same process
okay
the answer is 4x^3+6x^2+4x
hmm to make it easier lets make delta x=h so that delta y=(x+h)^4 - x^4 try solving that first
I cant follow my professor's teaching. Good to know that u are here to help me .thank you so much. you are a great´╗┐ help! i need to do more assignments about this so i will go out now .
the answer should be f'(x)=4x^3
haha im wrong
do the process i gave you there, and you will arrive at the correct answer ... :D
i wish i have a tutor like u hahaha .
remember this ?. (x+y)^4= x^4 +4x^3 y + 6 x^2 y^2 + 4x y^3 + y^4 make y an h here so that (x+h)^4= x^4 +4x^3 h + 6 x^2 h^2 + 4x h^3 + h^4
anyway thx a lot
goodbye!
ok just read it through here again and learn from it good luck and have fun now :D
ok
ok just messege me here and if you have prob i will go and give you an advise or correct if you have something done incorrectly ... :D

Not the answer you are looking for?

Search for more explanations.

Ask your own question