Question

Find first derivatives of following function. Simplify and leave answers in positive exponents :
q(z)=ln(4z+3)5z^3


Ans : 3/z + 4/4z+3

Sorry, I need help with the steps. I did product rule and I was kind of stuck at the simplifying part of the question .

Answer 1

y=uv
y'=uv'+u'v
d/dx (ln x )=1/x

Answer 2

Actually i know how to do it . I am actually stuck at the simplifying part towards the answer.

Answer 3

\[q'(z)=\frac{ 1 }{(4z+3)(5z ^{3})}(4z+3)[(3)(5)z ^{2}]+(5z ^{3})(4z)\]

Answer 4

my working and then i am stuck

Answer 5

So you found all the derivatives, right?

Answer 6

Yep I did . Just that I can't seem to simplify and get the answer right. It's just not my forte you see D:

Answer 7

Yes, use the chain rule along with product rule.

Answer 8

erm i mean how do i get to my final ans ... i just cant get the final ans which is suppose to be 3/z + 4/4z+3 ... I did cancelled out and done common denominators ...

Answer 9

Your derivative is correct, they just over simplified the problem to make it appear "neater". But if you perform the tedious algebra, you should get that answer.
That means, distribute and find the common denominator. Stuff which you should of already mastered in previous math courses.

Answer 10

Weird ... I did common denominator but couldn't get my answer. I will look into it again. Thks for the advice :)

Answer 11

\[q(z)=\ln(4z+3)5z ^{3}\]
=ln(4z+3)+ln5+3lnz
q'(z)=4/4z+3+0+3/z