z=(7x^4) * ln(x)4 where z and x are functions of t. (dx)/(dt)=4 when x=e. Calculate (dz)/(dt).

jiwekeegi

jiwekeegi

Open question

2022-08-21

I am struggling with an Implicit Differentiation question which is as follows:

z = ( 7 x 4 ) ln ( x ) 4 where z and x are functions of t. d x d t = 4 when x = e. Calculate d z d t .

What I have tried so far is finding d z d x which I believe is ( 7 x 3 ) + ( 28 x 3 ) ln ( x ) which I have used the chain rule to get this answer for d z d x .

This is the part where I have tried several things such as multiplying d z d x by d x d t but I'm not sure how that works and I have tried replacing the x's with e's and equation d x d t to d z d x but I am really unsure what I'm supposed to be doing in this question and nothing appears right.

Any help would be greatly appreciated.

Answer & Explanation

Jovany Mathews

Jovany Mathews

Beginner2022-08-22Added 8 answers

you are almost there. what you need is
d z d t = d z d x d x d t = ( 7 x 3 + 28 x 3 ln x ) | x = e d x d t = ( 7 e 3 + 28 e 3 ) 4 = 140 e 3

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