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