What is the derivative of x³? Show the steps.

Mathematics

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Answer

The derivative of x3x^3 is 3x23x^2.

Step-by-step solution

3 steps

Steps:
To find the derivative of x3x^3, we use the power rule for differentiation, which states that if f(x)=xnf(x) = x^n, then its derivative f′(x)=nxn−1f'(x) = nx^{n-1}.

  1. Identify n

    In the function f(x)=x3f(x) = x^3, the exponent nn is 3.

  2. Apply the power rule

    Substitute n=3n=3 into the formula nxn−1nx^{n-1}.
    f′(x)=3⋅x3−1f'(x) = 3 \cdot x^{3-1}

  3. Simplify the exponent

    f′(x)=3x2f'(x) = 3x^2

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