Fined the derivative of 10^-4*90/10^-4+6.

Oops, I mean 10^-4*90x/10^-4+6x.

The way you typed it ...

let y = (10^-4)(90x)/(10^-4) + 6x
= 90x + 6x
dy/dx = 90+6 = 96

To find the derivative of the given expression, we can start by simplifying the expression.

The expression is:

10^-4 * 90 / (10^-4 + 6)

To simplify the expression, let's work on the denominator first.

10^-4 + 6 = 0.0001 + 6 = 6.0001

Now, the expression becomes:

10^-4 * 90 / 6.0001

To find the derivative, we need to differentiate each term separately.

Differentiating 10^-4 gives us 0, since any constant raised to a constant power is always zero.

Differentiating 90 gives us 0 since it is a constant.

To differentiate the denominator, we need to recall the quotient rule for differentiation. The quotient rule states that the derivative of f(x)/g(x) is given by:

(f'(x) * g(x) - f(x) * g'(x)) / (g(x))^2

Let f(x) = 10^-4 and g(x) = 6.0001. Differentiating f(x) (which is a constant) gives us 0. Differentiating g(x) (which is also a constant) also gives us 0.

Applying the quotient rule, the derivative of the expression is:

(0 * 6.0001 - (10^-4 * 0)) / (6.0001)^2

Simplifying further, we have:

0 / (6.0001)^2

Which equals 0.

Therefore, the derivative of 10^-4*90/10^-4+6 is 0.