Derivative of c𝑥: Using the Power Rule for Differentiation

𝑑/𝑑𝑥[𝑐𝑥]

To find the derivative of 𝑐𝑥, where 𝑐 is a constant, we can use the power rule of differentiation.

To find the derivative of 𝑐𝑥, where 𝑐 is a constant, we can use the power rule of differentiation.

The power rule states that if we have a function of the form 𝑥^𝑛, its derivative is given by 𝑛𝑥^(𝑛−1).

In this case, 𝑥 is raised to the power of 1, so we can apply the power rule to find the derivative.

Taking the derivative of 𝑐𝑥 with respect to 𝑥, we get:

𝑑/𝑑𝑥[𝑐𝑥] = 𝑑/𝑑𝑥[𝑐] * 𝑥^1

Since 𝑐 is a constant, its derivative 𝑑/𝑑𝑥[𝑐] is 0.

So, 𝑑/𝑑𝑥[𝑐𝑥] = 0 * 𝑥^1 = 0.

Therefore, the derivative of 𝑐𝑥 with respect to 𝑥 is zero.

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