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Problem 55 Medium Difficulty

Find $ R'(0), $ where

$ R(x) = \frac {x - 3x^3 + 5x^5}{1 + 3x^3 + 6x^6 + 9x^9} $

Answer

$R^{\prime}(0)=1$

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Video Transcript

Hey, it's Claire. So when you right here. So we're gonna make effort. X be equal to UPS minus three. X cube plus five X to the fifth. We're gonna make G of X one plus three X cube plus six x to the sick plus nine x to the ninth power. So are derivative D R. Over D X is equal to the derivative of of of axe ones G FX minus the X Times, the derivative of GI effects Wilbur G of X Square. When we plug in zero, we get the Durban. She is zero minus zero. Oh, we're G of zero square and this becomes equal to when we substituted one.