Posted by **Yousef** on Saturday, October 22, 2011 at 7:24am.

Find the first derivative for the following functions

1) x^3 . sqrt( 3x^5 + 1 ) . sin (7x)

- Maths Calculus -
**Jai**, Saturday, October 22, 2011 at 8:17am
we can rewrite this as

sqrt(x^6)*sqrt(3x^5 + 1)*sin(7x)

sqrt(3x^11 + x^6)*sin(7x)

(3x^11 + x^6)^(1/2) * sin(7x)

then recall that derivative of two functions of x that are multiplied is equal to,

d/dx ( f(x)*g(x) ) = f'(x)g(x) + f(x)g'(x)

therefore,

(1/2)*(33x^10 + 6x^5)*(3x^11 + x^6)^(-1/2)*(sin 7x) + (3x^11 + x^6)^(1/2)*(7 cos 7x)

hope this helps~ :)

- Maths Calculus -
**Yousef**, Saturday, October 22, 2011 at 8:52am
thank u so much

helped me alot!!!!!

- Maths Calculus -
**Jackson**, Saturday, October 22, 2011 at 12:56pm
dude i love ur name :D

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