# Question Video: Finding the First Derivative of Polynomial Functions

Find the first derivative of the function π(π₯) = β2π₯ + 10.

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### Video Transcript

Find the first derivative of the function π of π₯ is equal to negative two π₯ plus 10.

If weβre given a function π of π₯ and want to find its first derivative π dash of π₯, then we need to differentiate the function. In this question, we are told that π of π₯ is equal to negative two π₯ plus 10. The general rule for differentiating states that if π of π₯ is equal to ππ₯ to the power of π, then π dash of π₯ is equal to πππ₯ to the power of π minus one. We multiply the power by the coefficient and reduce the power by one.

Negative two π₯ is the same as negative two π₯ to the power of one. Multiplying the power by the coefficient, one by negative two, gives us negative two. Reducing the power of π₯ by one gives us π₯ to the power of zero. π₯ to the power of zero is equal to one. This means that negative two π₯ to the power of zero is equal to negative two. Differentiating any constant gives zero. In this case, differentiating positive 10 is zero. If π of π₯ is equal to negative two π₯ plus 10, then π dash of π₯ is equal to negative two. The first derivative of the function is negative two.