The derivative of z which is either the one that we found earlier,

which was 1, or it would also apply this as the derivative of z to the first power

which is 1 times z to the zeroth power, which is also 1.

And 7 is simply a constant whose derivative is 0.

Therefore, I didn't write down the plus 0 part.

Now if you wanted to simplify this a bit, this is 15z squared + 4z- 1.

Next, let's look at 1 over z.

We can use the quotient rule for that one.

Even though there's also easier ways of finding this derivative, but

that's just fine by using the quotient rule.

So we square the denominators, z squared, we write down the denominator again,

that's z, times the derivative of the numerator, which is 0.

The numerators are constant.

Its derivative is 0.

Minus the numerator, 1, times the derivative of the denominator.

The derivative of z is 1.

The numerator there for simplifies to 1 with a negative sign in front of it.

The denominator is z squared.

So the derivative of 1 over z is -1 over z squared.

A different way of finding this derivative would have been to look at this function

as the function f of z = z to the power -1.

And realizing that this rule for

the derivative of z to the n also holds for negative exponents.

And so the derivative is therefore -1 times z to the n -1.

So -1 -1, which is -z to the -2, and

if you rewrite that, that is -1 divided by z squared.

Let's look at f(z) = (z squared- 1) to the nth power.

So here we have an inside function and

an another function on the outside to the power n.