Question

Find the derivative of the function.

http://www.webassign.net/cgi-bin/symimage.cgi?expr=g%28x%29%3Dint_%283%20x%29%5E%284%20x%29%20%28u%5E2-1%29%2F%28u%5E2%2B1%29%20du

Answer 1

derivative of the integral is the integrand. the trick here is to use the chain rule and break it into two pieces

Answer 2

\[\int_{3x}^{4x}f(t)dt=\int_{3x}^0f(t)dt+\int_0^{4x}f(t)dt\]

Answer 3

\[=-\int _0^{3x}f(t)dt+\int_0^{4x}f(t)dt\]

Answer 4

now use the fact that he derivative of integral is integrand. i will do second one, you can do first one

Answer 5

I have no idea how to solve it man

Answer 6

\[\frac{d}{dx}\int_0^{4x}\frac{u^2-1}{u^2+1}\]
\[=\frac{(4x)^2-1}{(4x)^2+1}\times 4\]
i just replaced u by 4x and then multiplied by the derivative of 4x which is 4. this is just the chain rule

Answer 7

really nothing could be easier. derivative of integral is integrand. so
\[\frac{d}{dx}\int_0^xf(t)dt=f(x)\] the only additional glitch here was you had 4x instead of x. so i replaced u by 4x in the integrand and then multiplied by 4, because that is the derivative of 4x. that is all

Answer 8

you can do the first one for yourself, it is identical but with 3x instead of 4x and a minus sign.

Answer 9

Where is the minus sign?