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Question 20 (1 point)Determine the derivative dx for y = -3tan(-x-4).6 3xsec? (-X- 4)d 3sec? (-x-4)k -Xsec 2(-x-4)d (~x-4) sec?(-x-4)...

Question

Question 20 (1 point)Determine the derivative dx for y = -3tan(-x-4).6 3xsec? (-X- 4)d 3sec? (-x-4)k -Xsec 2(-x-4)d (~x-4) sec?(-x-4)

Question 20 (1 point) Determine the derivative dx for y = -3tan(-x-4). 6 3xsec? (-X- 4) d 3sec? (-x-4) k -Xsec 2(-x-4) d (~x-4) sec?(-x-4)



Answers

Find the derivative of each of the given functions. $$y=(1-6 x)^{4}$$

When you're asked to find the derivative with respect to X. Of this problem, X squared y to the fourth. The first thing to point out is that you have a product in the year. So you need to do the product rule. And just a reminder with the product rule, uh, a lot of people leave the first piece, like to the left of the product alone times the derivative of the right side, which is you treat it like the power rule. You move the expo in front and subtract one from the exponent. But because we're differentiate with respect to X, it's kind of like the chain rule where you have to take the directive of why with respect to X. And then plus now you take the drift of of the left side because we didn't do that before and you leave that right side alone. Um so just to clean this up just a little bit and you might actually have a teacher, I want you to factor out because you can factor out a lot of things in here. Um You know, but for um for our purposes, I would just leave this the way it is, maybe rewrite the four X, squared y cubed just to, because multiplication is communicative and you might also have a teacher that asks you to um you know, you might have the two X. Y. To the fourth written first and then this piece, but there, this is a good answer.

Just let's take the derivative by using general. So we have oh, are power times Negative two. So that's 12 times 12 x occur to plus five and they have six minus one. So that's number seven times to do whatever inside. So that's 24 thanks.

All right. We want to find dy dx for the function. Why is equal to forge the power of six X to do So we're going to rely on relative shortcuts. We picked up from a single variable count, particularly those for exponential functions. So we have rules zero through three. Listen, here, rule zero on left is D B U D X is B. The U L n B D u D X. And also D the U D X equals to the U d u D X. Rules 123 other power product and change, respectively. We see that we're going to have to rely primarily on real zero to solve this derivative. So why equals 46 X is already it's most easily differential form B is for us six X. So by rule zero, dy dx is 4 to 6 X times Ln 4 10 6. Which we can simplify as six Ln 4 times 4- six x as is highlighted at the bottom.

In this problem, we are given If x equals two two x q minus four x square Last five X -6 it is first find F dash x differentiation of two X cube is two and two three x square. This is four into 2 x. And this is five differentiation of 60 because it's a constant. So this comes out us six x squared minus it takes plus right, it's differentiated again to get F double dash X. This is six into the transitional X squared is two x minus, It differences in access one and this is a constant. So no differentiation. So this becomes 12 X -8. That's


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