chi-chi asked in 科學數學 · 1 decade ago

四題大一微積分的計算

有四題寫不出來 幫忙一下 謝謝 (能解釋為什麼更好>"<

ln(2y)=e^y sin(9x)

dy/dx=?

x^5y=y^3x

dy/dx=?

a= sin^-1 (3/5 )

sec a = ?

rewrite the expression 6sinh(4 ln x) in terms of exponentials and simplify the result

6sinh(4 ln x) =?

4 Answers

Rating
  • rex
    Lv 7
    1 decade ago
    Favorite Answer

    1.ln(2y)= ey sin(9x)

    1/2y*2y'= ey*y'*sin(9x) 9ey*cos(9x)

    y'= dy/dx= 9eycos(9x)/[1/y- eysin(9x)]

    2.x5y= y3x 兩邊取對數

    5yln(x)= 3xln(y)

    5y'ln(x) 5y/x=3ln(y) 3x/y*y'

    y'= dy/dx= [3ln(y)-5y/x]/(5ln(x)-3x/y]

    3. a= sin-1(3/5)-->sin a=3/5 a:銳角

    -->sec a= 1/cos a= 1/√(1-sin2a)=5/4

    4.sinh x=(ex- e-x)/2-->

    6sinh(4lnx)=6*sinh(lnx4)

    =6*[eln(x^4)-e-ln(x^4)]/2

    =3*(x4-1/x4)

    that's all

    Source(s): rex
  • 1 decade ago

    應該是

    x^(5y)=y^(3x)

    要不然就可以對消了!

  • 1 decade ago

    第三題

    a= sin^-1 (3/5 )

    所以 sin a=3/5

    三邊為3.4.5的直角三角形

    又 sec a=1/(cos a)=5/4

  • 1 decade ago

    第二題是這樣x^(5y)=y^(3x) 還是 (x^5)y=(y^3)x

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