Calc

What are the derivatives? Thanks

a) y = log(base2)(4-9x)

b) y = x^(8x)

  1. 👍 0
  2. 👎 0
  3. 👁 76
  1. in general for y = loga u
    dy/dx = (1/ln a)(1/u)du/dx

    so for the above
    dy/dx = (1/ln2)(-9)/(4-9x)

    for the second one take ln of both sides
    y = x^(8x)
    ln y = ln (x^(8x))
    ln y = (8x)(ln x)
    now take the derivative implicityly using the product rule on the right side

    y'/y = 8x(1/x) + 8(ln x)
    y' = y[8 + 8ln x)
    = (8+8ln x)(x^(8x))

    1. 👍 0
    2. 👎 0
    posted by Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. Precalculus-Verify

    log(base2)x-log(base2)6= log(base2)5+ 2log(base2)3 log(x/6)=3log15 (x/6)=15^3 6*(x/6)=15^3*6 x=15^3*6 =20,250 Answer is 270.... What did I do wrong...

    asked by Melinda on January 30, 2012
  2. Calculus

    I have trouble finding the second derivative, my answer is a little off from the answer key. f(x)=(log(base2)x)^5 f'(x)=[5(log(base2)x)^4]/xln2 f"(x)=[20(log(base2)x)³(xln2)-(ln2+(x/2))(5(log(base2)x)^4)]/[x²(ln2)²] for the

    asked by sh on October 30, 2010
  3. Algebra

    In the logarithmic expression . . . log(base 4) 8 , how does the base 4 become base 2? Here is how it is suppose to be worked out: log(base2)8 / log(base2)4 => log(base2)2^3 / log(base2)2^2 => 3/2

    asked by Megan on November 16, 2013
  4. Algebra 2

    How would I solve the equation: log(base2)4 - log(base2)(x+3) = log(base2)8 ? i think i have to start by doing 4/(x+3)=8

    asked by Ana on February 28, 2010
  5. Calculus

    Find the second derivative of the following function: y=log(base2)x/x² y'=[(x/ln2)-2xlog(base2)x]/x^4 the derivative of x/ln2 is (ln2)^-1? y"={[((ln2)^(-1))-(2log(base2)x/xln2)]x^4-4x³[(x/ln2)-2xlog(base2)x]}/x^8 I tried

    asked by sh on October 31, 2010
  6. math

    Given that 2 log base2 (x+15) - log base2 x = 6 1.Show that x^2 -34x +225 = 0 2. Hence or otherwise solve the equation 2 log base 2 (x+15) - log base 2 x =6

    asked by lindsay on July 10, 2014
  7. Algebra 2

    solve the equation: log(base2)^(x-3)log(base2)^5 = 2log(base2)^10 I don't know how to solve it, can someone help me? Please and thank you.

    asked by Ana on February 28, 2010
  8. Math 12

    7. Simplify. b) log base2 20 + log base3 8 + log base2 3 + log base3 4 I can't remember how to switch bases... Thanks!

    asked by solexgirl12 on November 11, 2008
  9. Pre-Cal

    log base2 5 square root of 512 use the definition of b^1/n log base2 512^1/5 Not quite sure what to do after this Simplfiy.

    asked by jamie on January 10, 2010
  10. Maths

    Log base2(x+2)+log base4(y+10)=2 Log base4(x+2)+log base2(y+10)=5/2 Solve simultaneously

    asked by Rhonick on May 8, 2018

More Similar Questions