SOLUTION: calculate the first derivatives f(x) for each of the following: show all work A)f(x)= 2/3x3/4 + 3/4x2/3+ 5/6x2/3 B) f(x)= 2/5x3/2 + 5/6x3/4 + 5/6x3/2 C) f(x)= 3/4x2/3 +5

Algebra ->  Algebra  -> Test -> SOLUTION: calculate the first derivatives f(x) for each of the following: show all work A)f(x)= 2/3x3/4 + 3/4x2/3+ 5/6x2/3 B) f(x)= 2/5x3/2 + 5/6x3/4 + 5/6x3/2 C) f(x)= 3/4x2/3 +5      Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 63931: calculate the first derivatives f(x) for each of the following:
show all work
A)f(x)= 2/3x3/4 + 3/4x2/3+ 5/6x2/3
B) f(x)= 2/5x3/2 + 5/6x3/4 + 5/6x3/2
C) f(x)= 3/4x2/3 +5/6x3/2 + 3/4x3/2

Found 2 solutions by algebrapro18, funmath:
Answer by algebrapro18(206) About Me  (Show Source):
You can put this solution on YOUR website!
A)f(x)= 2/3x^(3/4) + 3/4x^(2/3)+ 5/6x^(2/3)
B) f(x)= 2/5x^(3/2) + 5/6x^(3/4) + 5/6x^(3/2)
C) f(x)= 3/4x^(2/3) +5/6x^(3/2) + 3/4x^(3/2)

A) f'(x) = (2/3 * 3/4)x^(-1/4) + (3/4 * 2/3)x^(-1/3) + (5/6 * 2/3)x^(-1/3)
= x^(-1/4)/2 + x^(-1/3)/2 + 5x^(1/3)/9
= 1/(2x^(1/4)) + 1/(2x^(1/3)) + 5/(9x^(1/3))

B) f'(x) = (2/5 * 3/2)x^(1/2) + (5/6 * 3/4)x^(-1/4) + (5/6 * 3/2)x^(1/2)
= 3x^(1/2)/5 + 5x^(-1/4)/8 + 5x^(1/2)
= 3x^(1/2)/5 + 5/(8x^(1/4)) + 5x^(1/2)

C) f'(x) = (3/4 * 2/3)x^(-1/3) + (5/6 * 3/2)x^(1/2) + (3/4 * 3/2)x^(1/2)
= x^(-1/3)/2 + 5x^(1/2)/4 + 9x^(1/2)/8
= 1/(2x^(1/3)) + 5x^(1/2)/4 + 9x^(1/2)/8

Answer by funmath(2925) About Me  (Show Source):
You can put this solution on YOUR website!
I am assuming that the fractions after the variables are exponents, let me know if I'm not interpretting you correctly:
calculate the first derivatives f(x) for each of the following:
show all work
A)f(x)= 2/3x3/4 + 3/4x2/3+ 5/6x2/3

f%28x%29=%282%2F3%29x%5E%283%2F4%29%2B%283%2F4%2B5%2F6%29x%5E%282%2F3%29
f%28x%29=%282%2F3%29x%5E%283%2F4%29%2B%289%2F12%2B10%2F12%29x%5E%282%2F3%29
f%28x%29=%282%2F3%29x%5E%283%2F4%29%2B%2819%2F12%29x%5E%282%2F3%29
f'(x)=%283%2F4%29%282%2F3%29x%5E%283%2F4-1%29%2B%282%2F3%29%2819%2F12%29x%5E%282%2F3-1%29
f'(x)=%281%2F2%29x%5E%28-1%2F4%29%2B%2819%2F18%29x%5E%28-1%2F3%29
f'(x)=1%2F2x%5E%281%2F4%29%2B19%2F18x%5E%281%2F3%29
:
B) f(x)= 2/5x3/2 + 5/6x3/4 + 5/6x3/2

f%28x%29=%282%2F5%2B5%2F6%29x%5E%283%2F2%29%2B%285%2F6%29x%5E%283%2F4%29
f%28x%29=%2812%2F30%2B25%2F30%29x%5E%283%2F2%29%2B%285%2F6%29x%5E%283%2F4%29
f%28x%29=%2827%2F30%29x%5E%283%2F2%29%2B%285%2F6%29x%5E%283%2F4%29
f'(x)=%283%2F2%29%2837%2F30%29x%5E%283%2F2-1%29%2B%283%2F4%29%285%2F6%29x%5E%283%2F4-1%29
f'(x)=%2837%2F20%29x%5E%281%2F2%29%2B%285%2F8%29x%5E%28-1%2F4%29
f'(x)=37%2Asqrt%28x%29%2F20%2B5%2F8%5E%281%2F4%29
:
C) f(x)= 3/4x2/3 +5/6x3/2 + 3/4x3/2

f%28x%29=%283%2F4%29x%5E%282%2F3%29%2B%285%2F6%2B3%2F4%29x%5E%283%2F2%29
f%28x%29=%283%2F4%29x%5E%282%2F3%29%2B%2819%2F12%29x%5E%283%2F2%29
f'(x)=%282%2F3%29%283%2F4%29x%5E%282%2F3-1%29%2B%283%2F2%29%2819%2F12%29x%5E%283%2F2-1%29
f'(x)=%281%2F2%29x%5E%28-1%2F3%29%2B%2819%2F8%29x%5E%281%2F2%29
f'(x)=1%2F2x%5E%281%2F3%29%2B19sqrt%28x%29%2F8
Happy Calculating!!!