The Power Rule: Finding the Derivative of 𝑥ⁿ with respect to 𝑥

𝑑/𝑑𝑥[𝑥^𝑛]

To find the derivative of 𝑥ⁿ with respect to 𝑥, we can use the power rule.

To find the derivative of 𝑥ⁿ with respect to 𝑥, we can use the power rule.

According to the power rule, the derivative of 𝑥ⁿ is given by: 𝑛𝑥ⁿ⁻¹.

Therefore, the derivative of 𝑥ⁿ with respect to 𝑥 is 𝑛𝑥ⁿ⁻¹.

For example, let’s say we have 𝑥². Using the power rule, we can find the derivative as follows:

Taking the derivative of 𝑥² with respect to 𝑥:
𝑑/𝑑𝑥[𝑥²] = 2𝑥^(2-1)
= 2𝑥

So, the derivative of 𝑥² with respect to 𝑥 is 2𝑥.

Similarly, if we have 𝑥³, we can find the derivative as follows:

Taking the derivative of 𝑥³ with respect to 𝑥:
𝑑/𝑑𝑥[𝑥³] = 3𝑥^(3-1)
= 3𝑥²

So, the derivative of 𝑥³ with respect to 𝑥 is 3𝑥².

In general, the derivative of 𝑥ⁿ with respect to 𝑥 is 𝑛𝑥ⁿ⁻¹.

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