Pre-Calculus

posted by .

Let f(x) = [(√x)-7]/[(√x)+7]. What is f'(x)?

What is the easiest way to find the derivative of this? Should I remove all the radicals and use quotient rule, like

f'(x)= ((x^0.5) + 7)(0.5x^-0.5) - ((x^0.5)-7)(0.5x^-0.5) / ((x^0.5) + 7)^2

Is this right? How do I simplify this? please show me thanks

  • Pre-Calculus -

    Radicals or exponents. Tomato, tomahto. Either way, it's slightly messy, but simplifies rather nicely.

    f = (√x-7)/(√x+7)
    As you say,
    f' = (1/2√x)(√x+7)-(√x-7)(1/2√x))/(√x+7)^2
    = (7/√x)/(√x+7)^2
    = 7/[√x(√x+7)^2)

  • Pre-Calculus -

    thank you

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Algebra 1

    Simplifying Radicals, Use the quotient property to simplify the expression. 3 times the square root of 6/3 3*sqrt(6/3) is the same thing as saying 3*sqrt(2) Your problem: 3√(6/3) is the same as 3√6/√3 To rationalize …
  2. amth/algebra

    can someone help me with simplification: ã20/5 - 1/ã5 my first answer is 1/ã5 my second answer is 10 -ã5/5 but the answere I have to choose from are: (a) ã20 - 5ã5/ã5 (b) ã20 - ã5/5 (c) cannot be simplified …
  3. Math

    Find an equation of the line that bisects the obtuse angles formed by the lines with equations 3x-y=1 and x+y=-2. a. (3√2 +√10)x-(√10 + √2)y-2√10+√2=0 b. (3√2 - √10)x+(√10 - √2)y+2√10+√2=0 …
  4. Calculus

    y=(√x)/((√x)+1) Find the concavity and point of inflection(s). y'=1/(√(x/2))(√x+1)² y'=1/(x√(x/2)+2√(x²/2)+√(x/2)) y"=0- ?
  5. maths

    I will be thankfull to you if you help me to solve the below problem: 6√x-11/3√x=2√x+1/√x+6 I tried to solve the above problem like this: (6√x-11)(√x+6)=(3√x)(2√x+1) 6√x(√x+6)-11(√x+6)=(3√x)(2√x)+(3√x)(1) …
  6. Math - Help with radicals please

    Please show work Simplify rational 1. 4√(a^6 b^13) / 4√(a^2b) 2.√(2x^3 / 49y^4) Add or Subtract 3. x√(75xy) - √(27x^3y) Multiply 4.(√(5) - 5) (2√(5) + 2) Rationalize the denominator 5. √(25x^5 …
  7. Pre-Calculus

    Find the slope of the tangent line to the curve √(1x+2y) + √(1xy) = 8.24 at the point (2,8)?
  8. Calculus

    How would I find the second derivative if f(x)= √(x^3+2) using the quotient rule. I got to the step where [(12x√(x^3+2))-(9x^4/√(x^3+2))]/4(x^3+2) how would i go from that to: (3x(x^3+8))/(4(x^3+2)^3/2)
  9. 8th grade algebra

    Can you check my answers? 1. 3√20/√4 = 3√(5)(4)/2 = 3(2)√5/2 = 3√5 2. 4√15/√9 = 4√15/3 3. √12/√16 = √4(3)/4 = 2√3/4 = √3/2 4. √10/√5 = √2
  10. Algebra

    1. Simplify the expression: 4√18+5√32 A.45√2 B.32√2 C.116√2 D.9√50 2. Simplify the expression: 7√5-3√80 A.-5√5 B.-4√75 C.-5 D.4√-75 3. Simplify the expression: √21(√3+√14) …

More Similar Questions