Answer:
To find the derivative of the function \(y = \frac{9}{8x^3}\), you can use the power rule for differentiation. The power rule states that if you have a function of the form \(y = ax^n\), where \(a\) and \(n\) are constants, then the derivative is given by:
\[y' = nax^{n-1}\]
In this case, \(a = \frac{9}{8}\) and \(n = -3\), since \(x^3\) is in the denominator. So, applying the power rule:
\[y' = \left(-3\right) \left(\frac{9}{8}\right) x^{-3-1}\]
Simplify the exponents and constants:
\[y' = -\frac{27}{8}x^{-4}\]
So, the derivative of the function \(y = \frac{9}{8x^3}\) is \(y' = -\frac{27}{8x^4}\).
Explanation: