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EEMajor12Best ResponseYou've already chosen the best response.0
f(x)=\int_1^{3x^5} \ln(t^2+1) \, dt
 2 years ago

satellite73Best ResponseYou've already chosen the best response.1
\[f(x)=\int_1^{3x^5} \ln(t^2+1) \, dt\]like that?
 2 years ago

satellite73Best ResponseYou've already chosen the best response.1
is the question find the derivative?
 2 years ago

imranmeah91Best ResponseYou've already chosen the best response.0
too hard to integrate
 2 years ago

satellite73Best ResponseYou've already chosen the best response.1
use the chain rule. the derivative of the integral is the integrand, so replace t by \[3x^5\] and then multiply the answer by \[15x^4\]
 2 years ago

EEMajor12Best ResponseYou've already chosen the best response.0
yeah im having trouble with these. Ill try it sat!
 2 years ago

satellite73Best ResponseYou've already chosen the best response.1
\[f'(x)=\ln((3x^5)^2+1)\times 15x^4\]
 2 years ago

satellite73Best ResponseYou've already chosen the best response.1
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?
 2 years ago

satellite73Best ResponseYou've already chosen the best response.1
if you need a word of explanation let me know
 2 years ago

EEMajor12Best ResponseYou've already chosen the best response.0
i understand chain rule for ln (function within function). where did the 15x4 come from?
 2 years ago

EEMajor12Best ResponseYou've already chosen the best response.0
15x^4 \ln(9x^{10}+1) ?
 2 years ago

satellite73Best ResponseYou've already chosen the best response.1
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
 2 years ago
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