Video: Finding the First Derivative of Polynomial Functions

Find the first derivative of the function 𝑓(π‘₯) = βˆ’2π‘₯ + 10.

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Video Transcript

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

If we’re given a function 𝑓 of π‘₯ and want to find its first derivative 𝑓 dash of π‘₯, then we need to differentiate the function. In this question, we are told that 𝑓 of π‘₯ is equal to negative two π‘₯ plus 10. The general rule for differentiating states that if 𝑓 of π‘₯ is equal to π‘Žπ‘₯ to the power of 𝑛, then 𝑓 dash of π‘₯ is equal to π‘›π‘Žπ‘₯ to the power of 𝑛 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 𝑓 of π‘₯ is equal to negative two π‘₯ plus 10, then 𝑓 dash of π‘₯ is equal to negative two. The first derivative of the function is negative two.

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