1. Find the first and second derivatives (y' and y”) for: A....

Transcript

00:01 Because there's so many problems here, i'm just going to jump right into the derivative notation, so i can reference back to it.

00:07 But 2e to the x cube power, because when you take the derivative of a constant in front, just goes along for the ride, the exponential part is itself.

00:20 You have to multiply by the derivative of the exponent.

00:23 It's a chain rule.

00:24 But you'll probably see teachers simplify this or write 2 times 3 in the x squared in front.

00:30 And i think from this point i'll probably just jump to the simplification of all of those where it's kind of obvious.

00:38 So in letter b, maybe this one, especially this one, e to the 3x because you also have to do the power product rule now.

00:50 Because the derivative of x is one and just make sure you leave e to the 3x alone.

00:54 Plus now you leave x alone times the derivative of e to the three x is itself.

01:00 Then you have to multiply by the derivative of 3x, which is 3.

01:04 So looking at the next one, where we have e to the negative x cubed over x.

01:12 E to the negative x cubed over x.

01:15 Well, now it's the quotient rule where you start with the derivative of the top, which again is itself.

01:23 But then we also like to leave, well, i'll go ahead and do this, maybe not simplify.

01:31 Take the derivative of the top of the exponent and leave the bottom alone minus.

01:37 Now you take the derivative of the bottom, leave the top alone all over the denominator squared.

01:44 Now, if anything, i would probably suggest students to rewrite something times x and add the exponent.

01:51 So it's going to be x cubed there.

01:53 But you didn't have to do what i just did...

Question

1. Find the first and second derivatives (y' and y'') for: A. $y = (2 + x)e^{-x^2}$ B. $y = \frac{\sin x}{x}$ C. $y = e^{-\sin x}$

Question

1. Find the first and second derivatives (y' and y'') for: A. $y = (2 + x)e^{-x^2}$ B. $y = \frac{\sin x}{x}$ C. $y = e^{-\sin x}$

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