Question

find the indicated derivative.
\\( \frac { d y } { d x } \\) if \\( y = - 9 x ^ { 3 } \\)
\\( \frac { d y } { d x } = \\)

Explanation:

Step1: Apply the power rule

The power rule states that if \( y = ax^n \), then \( \frac{dy}{dx}=anx^{n - 1} \). Here \( a=-9\) and \(n = 3\).

Step2: Calculate the derivative

Substitute \(a=-9\) and \(n = 3\) into the power - rule formula: \(\frac{dy}{dx}=(-9)\times3x^{3 - 1}\).
Simplify the expression: \(\frac{dy}{dx}=-27x^{2}\).

Answer:

\(-27x^{2}\)