How would you differentiate these problems?

Question

1) F(y) = ((2/y^2)-(3/y^4)) x (5y+4y^3)

2)R(t)=(t + 3e^t) x (3-√t)

3) y = (9t^2)/(8t^2-6t+5)

4) y(x) = (1)/(x+me^x)

5) y=e^x(5sinx + 6x) with respect to x.

if you could hos how you did each problem and what the answer was, it would be greatly appreciated!!!

Answer 1

1) F(y) = ((2/y^2)-(3/y^4)) x (5y+4y^3)
dF/dy = [((-4/y^3)-(-12/y^5)) x (5y+4y^3)] +
[(5+12y^2) x ((2/y^2)-(3/y^4)) ]

2)R(t)=(t + 3e^t) x (3-√t)
dR/dt = [(1+3e^t) x (3√t)] + [(3/2√t) x (t+3e^t)]

3) y = (9t^2)/(8t^2-6t+5)
dy/dt = [(18t) x (8t^2-6t+5) - (16t-6) (9t^2)] /
[(8t^2-6t+5)^2] just continue and simplify it :)

4) y(x) = (1)/(x+me^x) (m=constatnt number)
dy/dx = ((-1)(1+me^x)) / (x+me^x)^2

5) y=e^x(5sinx + 6x)
dy/dx= e^x(5sinx + 6x) + (5cosx+6) e^x =
e^x[5(sinx+cosx) +6x+6]

Answer 2

Since you are named after the philosopher Nietsche, you will appreciate my answer:

These PROBLEMS are DIFFERENTIATED by having DIFFERENT MATHEMATICAL FUNCTIONS in them.

I'm SO glad that you did not actually ask anyone to DIFFERENTIATE these FUNCTIONS. Phew! --- that would have been a problem of quite a different order.

You and I presumably both share this secret knowledge: that with Nietsche's precision in the use of language, he would have been looking forward to seeing how many people would fall into the logical trap of doing the latter problem.

Congratulations on setting this wonderfully inventive logical trap!

Live long and prosper.