Calculate Derivative of a function

[jweber]

Calculate the derivative of the function

g(z) = ((9z^2)/(6+z))^2

Find g'(z) =

Also Calculate dy/dx of the following function

y= (6x^2+x) (4x-x^2)

You do not need to expand answer.

Any help is greatly appreciated thank you.

Homework Equations

The Attempt at a Solution

 

[Char. Limit]

We don't do your homework for you, we help you with it. Now, what have you tried so far on the first one? Quotient rule seems to be the obvious choice...

 

[Fellowroot]

Also Calculate dy/dx of the following function

y= (6x^2+x) (4x-x^2)

Ok, I can give you some hints with this one.

You have two options:

1. Multiply (6x^2+x) (4x-x^2) out then take the derivative.

2. Use product rule

Hint for product rule let f(x)=(6x^2+x) and g(x)=(4x-x^2) then use the following formula

(dy/dx)=f '(x)g(x) + f(x)g '(x)

The first option may sound like the easy way out but don't depend on it completely.

What if you had to find (dy/dx) of y=(x^2)(Ln(x))

Now you have no choice but to use the second option and the formula.

Also, I would like for you to actually know what a derivative is.

What is a derivative? You need to know this.

I'm going to say it right here so NEVER forget it.

A derivative is the instantaneous slope on a graph at a specific point.

There are other explanations but at least know that one.

We also need to talk about (dy/dx)

What does (dy/dx) mean?

You can read it as the derivative of y with respect to x.

(dy/dx) is actually an implicit differentiation.

And don't forget that you can also call (dy/dx) as y '