아카이브 Show 등록된 기록 총 22,672,465 건 search < > 문서번호 : 9,476,483 의뢰정보 의뢰일시 : 2009년 08월 28일 (금요일) 11시 09분 의뢰인번호 : 106993 의뢰경로(또는 유형) : SMS문자 의뢰비용 : 200원 의뢰내용 : sec제곱을미분하면뭔가요?처리정보 처리일시 : 2009년 08월 28일 (금요일) 11시 33분 처리유형 : - 처리자 : deadqyn님 (-, 채택된지식 -개) 처리내용 : sec제곱, 즉, sec²θ에서 dθ에 대한 미분은 2secθ*(secθ)'이 되므로,(secθ'는 secθ*tanθ이므로), 답은 2sec²θ*tanθ이 되죠. (*는 곱하기인거아시죠?^^) 출처1 : http://expert.jisikman.com/taetkim/6042 검증결과 : 채택
미분 계산기미분할 함수를 입력하세요.:미지수: 미분 차수: 우측의 도함수 : sec(x)^2 to x = 2*sec(x)^2*tan(x) 단계별 풀이 보이기 그래프 보기. 식 바꾸기. 이 페이지에 직접 링크 값 x=derivative_help 구문 규칙 표시 미분 계산기 예제
© 2022 numberempire.com 모든 권리 보유함 미적분 예제인기 문제 미적분 Trouver la dérivée - d/dx y=sec(x^2) Step 1 , 일 때 는 이라는 연쇄 법칙을 이용하여 미분합니다. 자세한 풀이 단계를 보려면 여기를 누르십시오... 연쇄법칙을 적용하기 위해 를 로 바꿉니다. 를 에 대해 미분하면입니다. 를 모두 로 바꿉니다. Step 2 멱의 법칙을 이용하여 미분합니다. 자세한 풀이 단계를 보려면 여기를 누르십시오... 일 때 는 이라는 멱의 법칙을 이용하여 미분합니다. 인수를 다시 정렬합니다. The derivative of sec^2x is 2.sec^2(x).tan(x) There are two methods that can be used for calculating the derivative of sec^2x. The first method is by using the product rule for derivatives (since sec2(x) can be written as sec(x).sec(x)). The second method is by using the chain rule for differentiation. The product rule for differentiation states that the derivative of f(x).g(x) is f’(x)g(x) + f(x).g’(x) The Product Rule: First, let F(x) =
sec2(x) Then remember that sec2(x) is equal to sec(x).sec(x) So F(x) = sec(x)sec(x) By setting f(x) and g(x) as sec(x) means that F(x) = f(x).g(x) and we can apply the product rule to find F'(x) Using the product rule, the derivative of sec^2x is 2sec^2(x)tan(x) The chain rule is useful for finding the derivative of a function which could have been differentiated had it been in x, but it is in the form of another expression which could also be differentiated if it stood on its own. In this case: This means the chain rule will allow us to perform the differentiation of the expression sec^2x. Although the expression sec2x contains no parenthesis, we can still view it as a composite function (a function of a function). We can write sec2x as (sec(x))2. Now the function is in the
form of x2, except it does not have x as the base, instead it has another function of x (sec(x)) as the base. Let’s call the function of the base g(x), which means: g(x) = sec(x) From this it follows that: sec(x)2 = g(x)2 So if the function f(x) = x2 and the function g(x) = sec(x), then the function (sec(x))2 can be written as a composite function. f(x) = x2 f(g(x)) = g(x)2 (but g(x) = sec(x)) f(g(x)) = (sec(x))2 Let’s define this composite function as F(x): F(x) = f(g(x)) = (sec(x))2 We can find the derivative of sec^2x (F'(x)) by making use of the chain rule. The Chain Rule:
Now we can just plug f(x) and g(x) into the chain rule. How to find the derivative of sec^2x using the Chain Rule:
Using the chain rule, the derivative of sec^2x is 2.sec^2(x).tan(x) Finally, just a note on syntax and notation: sec^2x is sometimes written in the forms below (with the derivative as per the calculations above). Just be aware that not all of the forms below are mathematically correct.
To calculate the second derivative of a function, differentiate the first derivative. From above, we found that the first derivative of sec^2x = 2sec2(x)tan(x). So to find the second derivative of sec^2x, we need to differentiate 2sec2(x)tan(x). We can use the product and chain rules, and then simplify to find the derivative of 2sec2(x)tan(x) is 4sec2(x)tan2(x) + 2sec4(x) ► The second derivative of sec^2x is 4sec2(x)tan2(x) + 2sec4(x) Interesting property of the derivative of sec^2xIt is interesting to note that the derivative of sec2(x) is equal to the derivative of tan2(x). The derivative of: |
Sec 2 미분 - Sec 2 mibun
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