Question

Find F ′(x) for

Answer 1

a. -2xsin(x4)
b. sin(x4)
c. -sin(x4)
d. sin(32) - sin(x4)

Answer 2

@Michele_Laino

Answer 3

@aaronq @amistre64 @dan815 @freckles @ganeshie8 @inowalst @jagr2713 @Loser66 @Preetha @Michele_Laino

Answer 4

hint:
\[\Large F\left( x \right) = - \int_3^{{x^2}} {\sin \left( {{t^2}} \right)} \;dt\]

Answer 5

another hint: chain rule

Answer 6

i dont c how this is chain rule

Answer 7

try to differetiate the equation above. What do you get?

Answer 8

\[-\sqrt{\frac{ \pi }{ 2 }}(S(\sqrt{\frac{ 2 }{ \pi }}x ^{2})-S(3\sqrt{\frac{ 2 }{ \pi }}))\]

@Michele_Laino

Answer 9

i dont think this is right though...

Answer 10

no, it si more simple, we have to apply the fundamental theorem of integral calculus, in so doing we get:

\[\Large \frac{{dF}}{{dx}} = - \sin \left( {{x^4}} \right)\]

Answer 11

oops..it is more simple...

Answer 12

@familyguymath

Answer 13

@Michele_Laino is this it then?

Answer 14

yes! It is option C, as you can see

Answer 15

@Michele_Laino can u help me w/ another problem really quick?

Answer 16

ok!

Answer 17

here we have to separate the variables, so we can write this:
\[\frac{{dy}}{{dx}} = 3\frac{{dx}}{x}\]

Answer 18

oops.. I have made a typo, here is the right equation:
\[\frac{{dy}}{y} = 3\frac{{dx}}{x}\]

Answer 19

then we have to take the integral of both sides, what do you get?

Answer 20

@Michele_Laino