Understanding Derivatives: The Derivative of 𝑥 with Respect to 𝑥 is Always 1

𝑑/𝑑𝑥[𝑥]

The expression 𝑑/𝑑𝑥[𝑥] represents the derivative of the function 𝑥 with respect to 𝑥.

Ta

The expression 𝑑/𝑑𝑥[𝑥] represents the derivative of the function 𝑥 with respect to 𝑥.

Taking the derivative of 𝑥 with respect to 𝑥 may seem unnecessary because it will always be 1, but it is important to understand the concept of differentiation.

To find the derivative of 𝑥 with respect to 𝑥, we can use the power rule of differentiation. The power rule states that if we have a term 𝑥 raised to the power 𝑛 (where 𝑛 is a constant), the derivative of 𝑥ⁿ with respect to 𝑥 is given by 𝑛𝑥^(𝑛-1).

In our case, 𝑥 is raised to the power 1, so the derivative of 𝑥 with respect to 𝑥 is 1 multiplied by 𝑥^(1-1), which simplifies to 1 * 𝑥^0.

Since any non-zero number raised to the power of 0 is equal to 1, we get the final result:

𝑑/𝑑𝑥[𝑥] = 1 * 𝑥^0 = 1.

Therefore, the derivative of 𝑥 with respect to 𝑥 is equal to 1.

More Answers: