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Homework: Homework th Score: 0 of 1 pt4.5.7Find the derivativey= In Vx+5Enter YCUL &...

Question

Homework: Homework th Score: 0 of 1 pt4.5.7Find the derivativey= In Vx+5Enter YCUL &

Homework: Homework th Score: 0 of 1 pt 4.5.7 Find the derivative y= In Vx+5 Enter YCUL &



Answers

$7-46$ Find the derivative of the function.
$$y=10^{1-x^{2}}$$

So in this question are inter fashion. You is equal to three x squared waas seven thanks. And our outer function y is equal to u to the power of 10. So applying chain rule, do you? Why? Oh, we're x is going to be first you take d y over, do you, which is a derivative of U to the power 10. So that's gonna be 10 years to the power nine multiplied with do you over D X, which is the derivative of three X squared plus seven X, which is six. Thanks, Los seven. Now, to get the final answer, you just substitute the value of you into the equation. So your final answer will be 10 23 x squared, plus seven eggs to the power nine. No replied with six. Fix the glass cellar.

Wei have y equals free explosive on times Ellen of two X minus one. And we want to find the derivative. We're going day this by using the product rule. So why Prime equals the derivative of first thing, which is free Expo seven and will, um, time's just on to us. Press one untouched puss, huh? Three X plus seven times the derivative of on of two X minus one. So the derivative of three explosive Alan is just Paree. So we have three times Ellen two x minus one plus three x plus seven times and we're going to need to use the chain rule now. One over two X minus one Time's veteran of two x minus one. So then we have three times on two x minus one plus three x plus seven times two two x minus one

Huh? We will find a derivative of the function y equals three times X plus seven times natural delivery them off two times X minus one. And here we recognize the product of two function. So the river tive of why respected Ex Sequel to following the product rule single too Derivative Respect. Eggs off the first factor three times six plus seven and that times the second factor natural algorithm of 2 10 6 minus one plus the first factor three times six plus seven times the derivative Respect your ex off the natural algorithm off two times X minus one That is a sequel to the derivative here sequel to three in that time. So naturally, very them off two times six minus one plus three times X plus seven times on derivative Off the natural logarithms off this expression. Is he going to one over the expression that he's one over to 10 6 minus one minus one times the river tive respected ex off the argument of the natural religion Prettiest derivative respect. Very ex of 2 10 6 minutes one. And this is due to the shame rule that is equal to three times natural logarithms off to 10 6 minutes, one plus three times six plus seven times, one over two times six minus one times. And this derivative here cigarettes too. And so this is equal to if we want we can write this using the property softy Lower them as the natural algorithm of 2 10 6 minus one to the third plus. And here we have two times 3 10 6 months. Seven divided by 2 10 6 minus one. And so we can say that derivative off the given function respected X is equal to the natural algorithm. Off to time six minus one to the third, plus two times 3 to 3 time sex for seven, divided by two times six minus one

Suppose you want to differentiate the function Y. Which is equal to the product of tangent X. And co tangent X. And also we want to find the value of the derivative at the .11. Now to do this, we first note that the function can be rewritten into why which is equal to tanja next times Co Tangent X. Which is one over tangent X. And from here we can get rid of the tangent X. And So why is just equal to one differentiating dysfunction we have Why prime? Which is the derivative of one Is equal to zero. And so at the .11 we have. Why prime is also equal to zero because there is no X. Value there. So no matter what Point We have, the derivative is always zero. To verify this, we use a graphic utility, in which case we have the graph of the function Y. And its derivatives here, which is a horizontal tangent line whose slope is equal to zero. And so therefore The value of the derivative at 1 1 is zero.


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