Question

Find the first and second derivatives of the function. $f(x)=0.001 x^5-0.02 x^3$

    Find the first and second derivatives of the function.
$f(x)=0.001 x^5-0.02 x^3$
Single Variable Calculus: Early Transcendentals
Single Variable Calculus: Early Transcendentals
James Stewart,… 9th Edition
Chapter 3, Problem 49 ↓
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Find the first and second derivatives of the function. $f(x)=0.001 x^5-0.02 x^3$
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00:01 So since they're asking you for the first and the second derivative, i mean, i just expect that you know that the second derivative is simply the derivative of the derivative.
00:12 So in order to get the second derivative, you need the first derivative anyway.
00:18 But then you can just follow the power rule for the first derivative, where i may get an answer of 0 .005 x to the fourth, just to the fourth, just to.
00:31 Explain why you move that exponent in front and you multiply and then you subtract one from the exponent one i'll spell it out same thing with this one multiply and then subtract one and so that's why you get 0 .0 6 2 times 3 is 6 and then 3 minus 2 is 1 so that's your first derivative but now you need to do the same thing for the second derivative um it's the derivative of the derivative so you're still going to multiply coefficient with exponent and subtract 1.
01:08 So 5 times 4 is 20.
01:11 If it helps you, you can write 0 .20, but you don't need that second 0...
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