Question

Find the derivative dy/dx. y=7t cos (t^4) dt.

Answer 1

\[\int\limits_{0}^{\sqrt x} 7t \cos(t^4) dt\]

Answer 2

@satellite73 lol you are my favorite. This is my last one i promise.

Answer 3

i think i got 7cos t^4 -t(4t^3 sin(t^4)) for the derivative before I put in the sqrt of x

Answer 4

any ideas?

Answer 5

it the question to find the derivative of
\[\int\limits_{0}^{\sqrt x} 7t \cos(t^4) dt\]? if so , this is way easier than you think

Answer 6

yes.

Answer 7

did i get it correct above?

Answer 8

heck no
much much easier

Answer 9

ok.

Answer 10

before we do that, lets do this
what is the derivative of
\[\int\limits_{0}^{ x} 7t \cos(t^4) dt\]?

Answer 11

answer: the derivative of the integral is the "integrand" so it is simply
\[ 7x \cos(x^4) \]

Answer 12

oh so then you just plug in the squareroot?

Answer 13

what did i do? replaced every \(t\) in the integrand by an \(x\) because the integral is a function of \(x\)

Answer 14

close, but don't forget the "chain rule"

Answer 15

yo do not have
\[\int\limits_{0}^{x} 7t \cos(t^4) dt\] you have
\[\int\limits_{0}^{\sqrt x} 7t \cos(t^4) dt\]which is like a composite function
\[F(\sqrt{x})\]

Answer 16

so to take the derivative, replace every \(t\) by \(\sqrt{x}\) and then don't forget to multiply the result by the derivative of \(\sqrt{x}\) namely \(\frac{1}{2\sqrt{x}}\)

Answer 17

got it ?

Answer 18

so it is 7/2 cos x^2

Answer 19

lets see i didn't do it

Answer 20

oh sorry but thank you!

Answer 21

\[7\sqrt{x}\cos(\sqrt{x}^4)\times \frac{1}{2\sqrt{x}}\]
\[\frac{7}{2}\cos(x^2)\]

Answer 22

thank you it totally makes sense now!

Answer 23

yup, you got it
much easier than you thought i bet

Answer 24

i thougth about it wayy to hard.

Answer 25

it is math, don't think too hard

Answer 26

thank you!!

Answer 27

yw