1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Differentiate this equation!

  1. Jun 1, 2009 #1
    1: Sin(4x^2) * 8x

    2: Ln(3x) / x^2

    3: If dy/dx = 2ex and y=6 when x=0, then y =

    4: If ln(x^3) - ln(x) = 12, then x=e^(blank)

    5: evaluate the integral by integrating it in terms of an area
    (not sure how to use latex) integral from 1/2 -> 3/2 (2x-1)dx

    my attempts =]

    1: sin(4x^2)*8x
    using the chainrule for the first bit of the equation
    cos(4x^2)*8x
    which is cos(4x^2)*8x*8
    so 64x*cos(4x^2) is what i got

    2: ln(3x) / x^2
    using the quotient rule, lo*dhi - hi*dlo / lo^2
    differentiating ln(3x) using chain rule i get 3(ln(3x)), x^2 = 2x
    so quotient rule equation is
    ( (x^2)*3ln(3x) ) - (ln(3x) *2x) /(x^2)^2
    simplifying
    (x^2)(3ln(3x)) - ln(3x)*2x / x^8
    (x^2)(2ln(3x))-2x / x^8
    that's about as far as i got

    3: If dy/dx = 2ex and y=6 when x=0, then y =

    i tried to remember the old exponential differentiation rules,
    if C=e^x then ln(c) = x
    if c=ln(x) then e^x = x
    not quite sure how to solve it from there :)


    4: If ln(x^3) - ln(x) = 12, then x=e^(blank)
    is this one of those exponential rules?

    5: evaluate the integral by integrating it in terms of an area
    (not sure how to use latex) integral from 1/2 -> 3/2 (2x-1)dx
     
  2. jcsd
  3. Jun 1, 2009 #2

    rock.freak667

    User Avatar
    Homework Helper

    For 1) use the product law

    [tex]\frac{d}{dx}(uv)=v\frac{du}{dx}+u\frac{dv}{dx}[/tex]

    2) Use the fact that d/dx(lnx)=1/x.

    3) Integration is the reverse of differentiation. So d/dx(ex)=ex

    4) Use your rules of logarithms here

    5) Draw the line y=2x-1 and then draw x=1/2, then x=3/2. What figure do these lines and the x-axis form?
     
  4. Jun 1, 2009 #3
    thanks i've retried

    1: sin(4x^2) * 8x
    sin(4x^2) * 8 + cos(4x^2)*12x*8x
    8sin(4x^2) + 96x*cos(4x^2)
    is that right?

    2: ln(3x)/x^2
    (x^2 * 3/3x) - (ln(3x)*2x) / (x^2)^2
     
  5. Jun 1, 2009 #4
    3: If dy/dx = 2ex and y=6 when x=0, then y =

    d/dx is also 2e^x + c = 6

    2*e^x = 2, c=4
    2e^x + 4 = 6
    is this right?
     
  6. Jun 1, 2009 #5

    rock.freak667

    User Avatar
    Homework Helper

    Where did you get the 12x from in the second line of 1?
    2 looks correct

    ok if you know that when you differentiate ex with respect to x, you get ex+c.

    and you differentiate y with respect to x to get ex, what do you get?
     
  7. Jun 1, 2009 #6
    whoops should be 8x?
    sin(4x^2)*8 + (cos(4x^2)*8x)*8x
    8sin(4x^2)+(64x^2)*(cos(4x^2))
     
  8. Jun 1, 2009 #7
    5: evaluate the integral by integrating it in terms of an area
    (not sure how to use latex) integral from 1/2 -> 3/2 (2x-1)dx

    integral of 2x-1 = 2/2*x^2-x = (x^2)-x
    ((1.5^2)-1.5)-((0.5^2)-0.5) = 1

    is that right?
     
  9. Jun 2, 2009 #8

    rock.freak667

    User Avatar
    Homework Helper

    I believe when they say in terms of an area, you should draw out what the integral represents. Draw y=2x-1,x=1/2,x=3/2 on the same graph and find the area of the enclosed figure.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Differentiate this equation!
  1. Differential equations (Replies: 1)

  2. Differential equation (Replies: 4)

  3. Differential Equation (Replies: 12)

  4. Differential Equations (Replies: 1)

Loading...