Question

(5x^3-4)/(5x^4+1)
differentiate

Answer 1

i got
((5x^4) (15x^2) - (5x^3)(20x^3)) / (5x^4+1)^2

but it is suppose to be in the form (i am suppose to fill in the letters):

((-25x^A) + (Bx^3) + (Cx^D)) / (5x^4+1)^F

Answer 2

u=5x^3-4
u'=15x^2

v=5x^4+1
v'=20x^3

dy/dx = vu'-uv' / v^2
dy/dx = (5x^4+1)(15x^2)-(20x^3)(5x^3-4) / (5x^4+1)^2
dy/dx = (75x^6+15x^2)-(100x^6-80x^4) / (5x^4+1)^2
dy/dx = (-25x^6+80x^4+15x^2) / (5x^4+1)^2

Answer 3

how did you go from the second to last step to the last step?

Answer 4

second step to last step ? this is quotient rule
1st we will take numerator as u
2nd we will take denominator as v
3rd differentiate both to get u' n v'
4th use its formula, which is dy/dx = vu'-uv' / v^2
5th expand your numerator

then, by referring to your question, you're required to compare A, B and C with your answer, well, you got the value, what left now is simply take it, and compare the value of A, B and C with those who have same term :)

Answer 5

o i just didnt expand properly
thx

Answer 6

can you help me with another one please :):)