anonymous
  • anonymous
Integral Question
Mathematics
schrodinger
  • schrodinger
See more answers at brainly.com
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.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

anonymous
  • anonymous
f(x)=\int_1^{3x^5} \ln(t^2+1) \, dt
anonymous
  • anonymous
\[f(x)=\int_1^{3x^5} \ln(t^2+1) \, dt\]like that?
anonymous
  • anonymous
is the question find the derivative?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
yes it is,
anonymous
  • anonymous
how'd i guess?
anonymous
  • anonymous
too hard to integrate
anonymous
  • anonymous
use the chain rule. the derivative of the integral is the integrand, so replace t by \[3x^5\] and then multiply the answer by \[15x^4\]
anonymous
  • anonymous
yeah im having trouble with these. Ill try it sat!
anonymous
  • anonymous
\[f'(x)=\ln((3x^5)^2+1)\times 15x^4\]
anonymous
  • anonymous
i should have let you do it on your own, but once you see it you should realize how easy it is. it is clear what i did yes?
anonymous
  • anonymous
if you need a word of explanation let me know
anonymous
  • anonymous
i understand chain rule for ln (function within function). where did the 15x4 come from?
anonymous
  • anonymous
nvm 3x^5 derivative
anonymous
  • anonymous
15x^4 \ln(9x^{10}+1) ?
anonymous
  • anonymous
yes
anonymous
  • anonymous
it is the chain rule and you have a composite function. don't forget that \[F(x)=\int_a^x f(t)dt\] is a function of "x" so if you do not have an x in the upper limit, but rather something else, you have a composition like \[F(g(x))=\int_a^{g(x)}f(t)dt\] and so you need the chain rule

Looking for something else?

Not the answer you are looking for? Search for more explanations.