Question

calculate the derivative of cos(4xu)=3u+4x with respect to x

Answer 1

-4u sin(4xu) = 4, if u is not a function of x and is therefore considered a constant

Answer 2

if u is defined as a function of x, then u is not a constant but changes as x changes ....

Answer 3

-(4u+4xu') sin(4xu) = 3u' + 4 , if u is a function of x

Answer 4

it needs to be equal to u'(x)... so how would i write the answer?

Answer 5

since its u'(x) that tells me that u is a function of x so we can algebra the 2nd one into submission

Answer 6

first off, get it all into sums by distributing the sin thru

-4u sin(4xu) -4xu' sin(4xu) = 3u' + 4

now we can collect the u' stuff to one side and the other stuff to the other side

-4u sin(4xu) - 4 = 3u' + 4xu' sin(4xu)

and factor out the u'

-4u sin(4xu) - 4 = u' (3 + 4x sin(4xu))

and last we can divide off the u' baggage to get it all alone

\[\frac{-4u\ sin(4xu) - 4}{3 + 4x\ sin(4xu)} = u'\]

and with any luck, its good :)

Answer 7

thanks!

Answer 8

yep, hopes it right; i do have a tendency to get mixed up in the mathing part ;)