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Problem 28 Medium Difficulty

(a) If $ f(x) = e^x $ cos $ x, $ find $ f'(x) $ and $ f"(x). $
(b) Check to see that your answers to part (a) are reasonable by graphing $ f, f,' $ and $ f". $


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Video Transcript

it's queer. So then you read here. So we have. Why is equal to eat the X go sign. So using the product rule for the first derivative, we get the derivative or eat the X, which is each the ex turns co sign and then we take the derivative of co sign, which is negative sign times each of X. This gives us each the eggs terms CO signed minus sign. We're going to start with the second derivative, So we're gonna use the product rule again when we go eat to the eggs. Times Co sign minus sign Derivative plus the derivative of E to the X Times CO sign minus sign. This gives us eat the axe times negative sign minus co sign plus E to the X terms CO sign minus sign, which gives us negative to e to the X sign report be we're gonna do a graft. So we're gonna start with our original equation who looks something like this, Then our first year of it is then our second derivative. You let me fix this. Look, I'm doing We're like that