Find the first derivative for the following functions

Question

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

Answer 1

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~ :)

Answer 2

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helped me alot!!!!!

Answer 3

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