Video Transcript
Find the first derivative of the function 𝑓 of 𝑥 is equal to negative two 𝑥 plus 10.
If we’re given a function 𝑓 of 𝑥 and want to find its first derivative 𝑓 dash of 𝑥, then we need to differentiate the function. In this question, we are told that 𝑓 of 𝑥 is equal to negative two 𝑥 plus 10. The general rule for differentiating states that if 𝑓 of 𝑥 is equal to 𝑎𝑥 to the power of 𝑛, then 𝑓 dash of 𝑥 is equal to 𝑛𝑎𝑥 to the power of 𝑛 minus one. We multiply the power by the coefficient and reduce the power by one.
Negative two 𝑥 is the same as negative two 𝑥 to the power of one. Multiplying the power by the coefficient, one by negative two, gives us negative two. Reducing the power of 𝑥 by one gives us 𝑥 to the power of zero. 𝑥 to the power of zero is equal to one. This means that negative two 𝑥 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 𝑥 is equal to negative two 𝑥 plus 10, then 𝑓 dash of 𝑥 is equal to negative two. The first derivative of the function is negative two.
