Video: Finding the First Derivative of a Linear Function

Given that 𝑦 = −25𝑥, determine d𝑦/d𝑥.

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Video Transcript

Given that 𝑦 is equal to negative 25𝑥, determine d𝑦 by d𝑥.

In order to work out d𝑦 by d𝑥, we need to differentiate the function with respect to 𝑥. The general rule for differentiating states that if 𝑦 is equal to 𝑎 multiplied by 𝑥 to the power of 𝑛, then d𝑦 by d𝑥 is equal to 𝑛𝑎 multiplied by 𝑥 to the power of 𝑛 minus one. We multiply the power by the coefficient and reduce the power by one.

In this question, 𝑦 is equal to negative 25𝑥. This is the same as negative 25𝑥 to the power of one. In order to differentiate this function, our first step is to multiply the power, one, by the coefficient negative 25. This is equal to negative 25. Reducing the power by one gives us 𝑥 to the power of zero. Any number or letter to the power of zero is equal to one. In this case, 𝑥 to the power of zero equals one.

Negative 25 multiplied by one is equal to negative 25. Therefore, d𝑦 by d𝑥 equals negative 25. If 𝑦 is equal to negative 25𝑥, then d𝑦 by d𝑥 equals negative 25.

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