another derivative question...?

Question

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

this becomes F(y) = [1(y^-2) - (3(y^-4)] (y+5y^3)

this is what I've solved so far:

F ' (y) = [-2(y^-3)+12(y^-5)] (y+5y^3) + [1(y^-2) - 3(y^-4)](1+15y^2)

I don't know if I've done this correctly at all !!!
The answer should be

F ' (y) = 5 + 14/y^2 + 9/y^4

Could someone please explain this to me. I am struggling taking an online calculus class but I am really making an effort to learn HOW to do the problems. I am just having a hard time with the algebra!

Answer 1

f(y) = [ y^(-2) - 3.y^(-4) ].[ y + 5y³ ]

Using product rule:-
f `(x) =
[ -2y^(-3) + 12y^(-5)].[ y + 5y³ ]
+ [(1 + 15y²).(y^(-2) - 3y^(-4) ]

-2y^(-2) - 10 + 12y^(-4)
+ 60y^(-2) + y^(-2) - 3y(-4) + 15 - 45y^(-2)

14y^(-2) + 5 + 9y^(-4)

5 + 14/y² + 9/y^4

Answer 2

The most straighforward method is to expand the original function, and differentiate the individual pieces:
y/y^2 + 5y^3/y^2 - 3y/y^4 -15y^3/y^4 = 1/y + 5y - 3/y^3 -15/y =
5y - 3/y^3 - 14/y. Now take derivatives of each part, using the power rule as needed (for the second and third parts):
5 + 9/y^4 + 14/y^2

Answer 3

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

applyin product rule....nd solvin
f'(y)= (y+5y^3)[(-2/y^3) + (12/y^5)]+[(1/y^2) - (3/y^4)](1+15y^2)
now simplyifin n solvin....
f'(y)= -2/y^2 + 12/y^4 - 10 + 60/y^2 + 1/y^2 - 3/y^4 + 15 -45/y^2
f'(y)=5 + 14/y^2 + 9/y^4 ans ....

Answer 4

F(y) = [(1/y^2) - (3/y^4)] (y+5y^3)
F(y) = 1/y + 5y - 3/y^3 - 15/y
F (y) = 5y - 3/y^3 - 14/y
F ' (y) = 5 +9y^-2 - 14 ln(y)

Answer 5

F(y) = [(1/y²) - (3/y⁴)] [y+5y^3]
F(y) = [(y-²) - (3y-⁴)] [y+5y^3]
F(y) = [ y-¹ - 3y^-3 + 5y -15y-¹ ]
F(y) = [+ 5y -14y-¹ - 3y^-3 ]
d/dy = + 5 + 14y-² + 9y-⁴
d/dy = + 5 + 14/y² + 9/y⁴

Answer 6

the derivative is correct. you should get the correct answer with some careful algebra...

Answer 7

if y(x)=f(x).g(x) then dy/dx=(df/dx).g+(dg/dx).f => d((x^two).(e^x))={d(x^two)/dx}.(e^x)+(x^two).{... 2x.e^x+x^two.e^x = x.e^x (two+x) Similarly for the moment spinoff, d{(2x.e^x)+(x^two.e^x)}/dx= (2e^x+ 2xe^x)+(2xe^x+x^2e^x) = e^x (two+4x+x^two)