The Power Rule of Differentiation: How to Find the Derivative of c𝑥

𝑑/𝑑𝑥[𝑐𝑥]

To differentiate 𝑐𝑥 with respect to 𝑥, we can apply the power rule of differentiation. T

To differentiate 𝑐𝑥 with respect to 𝑥, we can apply the power rule of differentiation. The power rule states that if we have a function of the form 𝑎𝑥ⁿ, where 𝑎 is a constant and 𝑛 is a real number, then the derivative is given by 𝑛𝑎𝑥ⁿ⁻¹.

In this case, we have 𝑐𝑥, where 𝑐 is a constant. We can think of this as 𝑐 multiplied by 𝑥 raised to the power of 1. Therefore, applying the power rule, we can find the derivative as follows:

𝑑/𝑑𝑥[𝑐𝑥] = 1 × 𝑐 × 𝑥^(1-1) = 𝑐 × 𝑥^0

Now, any number raised to the power of 0 is equal to 1, so we have:

𝑑/𝑑𝑥[𝑐𝑥] = 𝑐 × 1

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

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