find-the-derivative-of-the-following-functions-y5-x2cos-x

Question

Find the derivative of the following functions.
$$y=5 x^{2}+\cos x$$

Theresa Nguyen · Accepted Answer

we are looking for The derivative of y is equal to five x squared plus Co sign of X to know Tate that we want a derivative. It&#x27;ll look like D over DX of why is equal to D over DX of five X squared plus Co. Sign of X instead of using an D x D over DX of why you can also do Why prime Too short and your notation So now we are looking for the derivative of five X squared plus coastline X D over DX of five X squared plus coastline elex. To find this, we want to use the some difference rule to break apart the derivatives that will look like F plus minus. G prime is equal to F prime plus minus G prime. Already. To break this down, it&#x27;ll look like D over DX of five X squared plus D over DX of CO Sign X. We&#x27;re first going to look for our five x squared D over DX of five X squared. That will be done first when you take out the constant so it&#x27;ll look like five over D over DX of X squared to find the derivative of X squared. We&#x27;re going to use the power rule D over DX of X to the A A in this case is, too, that is equal to a Times X to the A minus one. This will look like five times two x to the Tu minus one, which is 10 X. Our next derivative is D over DX of CO sign of X, which is a negative sign of X. Let&#x27;s put this all together. Are y prime is equal Teoh 10 x minus Sign of X instead of using why prime, you can also do d over DX of why is equal to 10 x minus sign of X.

Louisa Benatovich · Answer

derivative of F of X equals. X Times Coach on five X squared When you have a function, are variable affection with variable times. Another function with the variable. You use the product rule. Never forget the product rule I cannot write. Got a cruel, which is the first becomes a derivative of the second across the second times the derivative of the first. We&#x27;re saying that the first is you and the second is OK, but first X times, the derivative of the second. Now this is where it&#x27;s complicated. We&#x27;ve got 456 So the derivative of co sign DDX of co sign of coastline X is negative science. So here the variable isn&#x27;t just exit five X squared. So it&#x27;s like saying times negative sign of five X squared. But inside this function, you have in no other functions you have to take the derivative of that the derivative of five X squared. You know that one that&#x27;s just 10 x perfect. So we have the first part down. You re prime the first times the derivative of the second plus the second, which isn&#x27;t easy. We can just rewrite this complicated thing. Khost find five X squared. This is the second part times The derivative of the first derivative of X is just one, so there&#x27;s no need to write it. Let&#x27;s like this a little bit prettier for guest primal primal vaccine pools. It&#x27;s nice to put the least complicated things in the front, so we have the X, and we have a little negative one in front of here. The tenants. This is the way I write it. It doesn&#x27;t really matter. So it&#x27;s like saying I get a 10 x squared because we have extracts accident like X squared plus y squared.

Todd Vawdrey · Answer

for this problem, we&#x27;re gonna find the derivative of the CO sign of Fifth to the X. So in order to do this, we&#x27;re gonna take the derivative of assigned 50. The ex were going. He used the chain rule right here. So the first thing we&#x27;re gonna do is take the derivative of the to the fifth function that we have right here. We&#x27;re going to apply the power rule and get five co signed to the fourth ex on and that. So we lowered the power by one here, and then we need to take the derivative of the inside, which is actually the co sign of X. So we&#x27;re gonna multiply that by the derivative, which is the negative sign of X. So altogether, we get that the derivative, uh, is negative. Five. Sign ex co signed to the fourth ex right there.

Shumayal N · Answer

questions like this one. Where and you have functions within functions. You start from the outermost function and you work your way in. So the first thing we&#x27;re gonna take care of and this question is the power. So using the power will we get five Sign four and everything else you just right as it is. So coastline three x you right as it is, the next function as you go in is sign. So the derivative of sign is co sign and everything else again, you write the same way now, working away inward. The next function is co signed three of X, so the derivative of co sign is minus sign three of X. And then finally you take the derivative off three of X, which is three. So you can rewrite this five into three and there&#x27;s a minus. Sign DSM minus 15 and then sign three of X into co sign co signed through your legs into signing to the power for co sign three of X

Romaila Saud · Answer

we can use change will in order to find the derivative off y equals costs off five t Let&#x27;s identify the interim out of functions. First, the Inter function you is equal to five t and the upper function. Why is equal to costs a few next less. Let&#x27;s evaluate D U by d. T, which is equal to fi. Divide by D&#x27;You is evaluated as minus sign off you by changeable. We already know that de vie by d t should be equal to de vie by the u in two d u by d. T. All we have to do now is to replace the values that we&#x27;ve already calculated. D y by D. U is replaced by minus Sign off you and do you buy DD evaluated as five is replaced. Next we put in the value off you. Hence the final answer becomes minus five. Sign off five t

Sid Wan · Answer

twenty two we have. Why was three co sign x Our far Mona&#x27;s? Cause I look thiss car looks We just need to use quotient plus Lina&#x27;s cause I square top on Derivative is back You sri sai acts What price for the war. So frak bottom What directive is fine? What a black top one Sorry, because I and that&#x27;s it because somebody five Barton laws like fifteen sign at plus three side at cause I eggs coz some tracks race Okay, he&#x27;s got cancer, fathers, mothers, coastline where, like fifteen

Problem

Find the derivative of the following functions. $…

Problem 24 Easy Difficulty

Find the derivative of the following functions.
$$y=5 x^{2}+\cos x$$

Answer

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William Briggs, Lyle Cochran, Bernard GilletCalculus Early Transcendentals

Grace H.

Anna Marie V.

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Calculus Early Transcendentals