Question

In Exercises \(31-42,\) find \(d y / d x\). $$y=x^{9 / 4}$$

Short answer

The derivative of the given function \(y = x^{9 / 4}\) is \(d y / d x = 9 / 4 \cdot x^{5 / 4}\).

Step-by-step solution

Identify the power of x in the given function

In the given function, \(y = x^{9 / 4}\), the power of \(x\) is \(9/4\).

Apply the power rule to find the derivative

The power rule states that the derivative of \(x^n\) is \(n \cdot x^{n-1}\). Therefore, according to the power rule, \(d y / d x = 9 / 4 \cdot x^{9 / 4 - 1}\).

Simplify the expression

Simplify \(d y / d x = 9 / 4 \cdot x^{5 / 4}\).