Question

Find the derivative:

Answer 1

\[\frac{ d }{ dx}\int\limits_{2}^{x}\ln(t^2+1)dt\]

Answer 2

i need some help to work through it!

Answer 3

\[\large\frac{\mathrm d}{\mathrm dx}\int\limits_{h(x)}^{g(x}f(t)\mathrm dt=f\big(g(x)\big)\cdot g'(x)-f\big(h(x)\big)\cdot h'(x)\]

Answer 4

*g(x)

Answer 5

is that the general rule?

Answer 6

I think it is called the fundamental theorm of calculus or somesuchnonsense

Answer 7

my book uses the second fundamental theorem for this chapter haha

Answer 8

This ol'thing?\[\frac{\mathrm d}{\mathrm dx}\int\limits_{h(x)}^{g(x)}f(x,t)\mathrm dt=f\big(g(x)\big)\cdot g'(x)-f\big(h(x)\big)\cdot h'(x)+\int\limits_{h(x)}^{g(x)}\frac{\partial f(x,t)}{\partial x}\mathrm dt\]

Answer 9

its this , the second fundamental theorem for constructing antiderivatives \[F(x)=\int\limits_{a}^{x}f(t)dt\]

Answer 10

the derivative of the integral is the "integrand"

Answer 11

\[\frac{ d }{ dx}\int\limits_{2}^{x}\ln(t^2+1)dt\] replace \(t\) by \(x\) and get \[\frac{ d }{ dx}\int\limits_{2}^{x}\ln(t^2+1)dt=\ln(x^2+1)\] that is all

Answer 12

@satellite73 wow that is all? It looks kind of intimidating at first to tell you the truth but this seems pretty easy

Answer 13

yes, it is pretty easy, the question is only checking if you know that the derivative of the integral is the integrand
that is all

Answer 14

sounds good