SOLUTION: Hi :o) This is another calculus question but again it's the fractional algebra stuff that I'm unsure of.: Differentiate y = (5x³ + 7x)^1/4 I managed to get to the point of

Algebra ->  Rational-functions -> SOLUTION: Hi :o) This is another calculus question but again it's the fractional algebra stuff that I'm unsure of.: Differentiate y = (5x³ + 7x)^1/4 I managed to get to the point of       Log On


   

Question 260674: Hi :o)
This is another calculus question but again it's the fractional algebra stuff that I'm unsure of.:
Differentiate
y = (5x³ + 7x)^1/4
I managed to get to the point of
dy/dx = 1/4(15x³ + 7)/(5x³ + 7x)^3/4
but not sure if it's right or if I can go any further than this answer.
Thanks again!
manda
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Substitute
u=5x%5E3+%2B+7x
y=u%5E%281%2F4%29
Then the chain rule,
dy%2Fdx=%28dy%2Fdu%29%28du%2Fdx%29
dy%2Fdu=%281%2F4%29u%5E%28-3%2F4%29
du%2Fdx=15x%5E2%2B7
dy%2Fdx=%281%2F4%29%2815x%5E2%2B7%29%2F%285x%5E3%2B7x%29%5E%283%2F4%29
You have a mistake on the exponent of 15x^2 in the numerator.
I think that's as reduced as possible.