Ask your own question, for FREE!
Mathematics 8 Online
OpenStudy (anonymous):

Calculate the following derivatives \[\frac{d}{dx} \int_0^x dt \cos(t^{3}+1)\]

OpenStudy (lgbasallote):

\[\large \frac{d}{dx} \int_0^x dt \cos(t^{3}+1)\]

OpenStudy (lgbasallote):

interesting

OpenStudy (anonymous):

thanks i forgot to add math signs now is ok

OpenStudy (amistre64):

use the definition from ftc

OpenStudy (anonymous):

i need complete solution guys i have exam on friday i cant trust my own solution..

OpenStudy (anonymous):

thanks @lgbasallote i was unable to read it . so by using first form Fundamental theorem of calculus it is (derivative and integral gets cancelled ) cos(x^3+1)

OpenStudy (anonymous):

use this \[\frac{d}{dx} \int\limits_{a(x)}^{b(x)} f(t) dt= f(b(x)) \ b'(x)- f(a(x)) \ a'(x) \]

OpenStudy (amistre64):

\[y=f'(x)\] by using the definition of a definite integral we get \[\int_{a(x)}^{b(x)}(y=f'(x))\to\ f(b(x))-f(a(x))\] by using the chain rule we get \[\frac{d}{dx}[f(b(x))-f(a(x))]=f'(b(x)b'-f'(a(x)))a'\]

OpenStudy (amistre64):

i gots too many paranthesis lol

OpenStudy (anonymous):

and how looks solution of my question according this formulas ?

OpenStudy (amistre64):

well, you now f'(x) and a(x) and b(x) soo use them

OpenStudy (anonymous):

ok thanks i take a look at it, i hope i can do ;)

OpenStudy (amistre64):

if not, dont worry; we can then help out some more

OpenStudy (anonymous):

ok thank you

OpenStudy (anonymous):

\[ \frac{d}{dx} \int_0^x f(t) dt=f(x)\text{ by the FTC, so }\\ \frac{d}{dx} \int_0^x \cos(t^{3}+1) dt=\cos(x^{3}+1) \]

OpenStudy (anonymous):

thank you very much Mr Saab can you say me pls what FTC is ?

OpenStudy (anonymous):

@tunahan FTC(fundamental theorem of calculus ) is it is a relation between derivative and integrals

OpenStudy (anonymous):

@sami thank you

Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!
Latest Questions
laylasnii13: Who wanna write or make a song with me???
3 hours ago 0 Replies 0 Medals
kaelynw: art igg
2 hours ago 9 Replies 1 Medal
XShawtyX: Art
21 hours ago 6 Replies 0 Medals
Nina001: teach me how to draw or just tell me the basics
23 hours ago 2 Replies 1 Medal
XShawtyX: We doing another drawing gimme ideas to add to this
1 day ago 9 Replies 1 Medal
RAVEN69: What is x 3+y 3+z 3=k
1 day ago 20 Replies 1 Medal
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!