Question

Integral Question

Answer 1

f(x)=\int_1^{3x^5} \ln(t^2+1) \, dt

Answer 2

\[f(x)=\int_1^{3x^5} \ln(t^2+1) \, dt\]like that?

Answer 3

is the question find the derivative?

Answer 4

yes it is,

Answer 5

how'd i guess?

Answer 6

too hard to integrate

Answer 7

use the chain rule. the derivative of the integral is the integrand, so replace t by
\[3x^5\] and then multiply the answer by
\[15x^4\]

Answer 8

yeah im having trouble with these. Ill try it sat!

Answer 9

\[f'(x)=\ln((3x^5)^2+1)\times 15x^4\]

Answer 10

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?

Answer 11

if you need a word of explanation let me know

Answer 12

i understand chain rule for ln (function within function). where did the 15x4 come from?

Answer 13

nvm 3x^5 derivative

Answer 14

15x^4 \ln(9x^{10}+1) ?

Answer 15

yes

Answer 16

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