Question: "What is the derivative of x3"

Maria Huey

Answered question

2021-12-21

What is the derivative of

x^{3}

Ethan Sanders

Beginner2021-12-22Added 35 answers

The derivative of

x^{3}

can be found using the power rule, which can be applied to polynomials of the form

a x^{n}

. When the coefficient of

x

is larger than one, the two numbers are multiplied together.
The power rule states:

\frac{d}{d x} [a x^{n}] = n a x^{n - 1}

where

a, n

are constants
So for the derivative of

x^{3}

, since the coefficient is 1, then the number does not change. The coefficient is 3 because

1 \times = 3

, and the exponent is reduced by 1.
Hence,

\frac{d}{d x} [x^{3}] = 3 x^{2}

lovagwb

Beginner2021-12-23Added 50 answers

Possible derivation:

\frac{d}{d x} (x^{3})

Use the power rule,

\frac{d}{d x} (x^{n}) = n x^{n - 1}

, where

n = 3

\frac{d}{d x} (x^{3}) = 3 x^{2}

:
Answer:

= 3 x^{2}

2021-12-27

Both answers are good!

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