y=x 3 y, equals, x, cubedwhat is 𝑑𝑦𝑑𝑥dxdy​ start fraction, d, y, divided by, d, x, end fraction?

Break Down the Problem

1. Identify the function given: $y = x^3$.
2. Determine what is required: Find $\frac{dy}{dx}$.

Relevant Concepts

1. The derivative of a function represents the rate of change of that function with respect to its variable.
2. Use the power rule of differentiation: If $y = x^n$, then $\frac{dy}{dx} = n \cdot x^{n-1}$.

Analysis and Detail

1. For our function $y = x^3$:
   • Here, $n = 3$.
2. Applying the power rule: $\frac{dy}{dx} = 3 \cdot x^{3-1} = 3x^2$

Verify and Summarize

• The differentiation has been applied correctly according to the power rule.
• The result is straightforward, confirming that the calculations are accurate.

Final Answer

$\frac{dy}{dx} = 3x^2$