Does my answer look correct?
Find the derivative.
11, y= (e^3-e)(e+5)/6e
my work:
((6e)(4e^3 + 15e^2 - 2e - 5) - (6)(e^4 + 5e^3 - e^2 - 5e))/ (6e)^2
Multiplied/divided everything through
My answer:
(10e^2 + 30e - 3)/ 18
I cant follow your work:
I assume e is a derivative.
(e^3-e)(e+5)/6e
1/6e * (e^4 + 5e^3 -e^2 - 5e)
1/6 * (e^3 + 5e^2 -e-5 )
derivative:
dy/de = 1/6 (3e^2+10e -1)
check my work.
To find the derivative of the given function, let's break it down step by step.
First, the original function is:
y = (e^3 - e)(e + 5) / 6e
To simplify, let's expand the numerator:
y = (e^4 + 5e^3 - e^2 - 5e) / 6e
Next, we can distribute the 1/6e to each term in the numerator:
y = (1/6e)(e^4) + (1/6e)(5e^3) - (1/6e)(e^2) - (1/6e)(5e)
Simplifying further:
y = (1/6)(e^3) + (5/6)(e^2) - (1/6)(e) - (5/6)
Finally, to find the derivative, we differentiate each term with respect to e:
d/dx [(1/6)(e^3)] = 1/6 * 3e^2 = e^2/2
d/dx [(5/6)(e^2)] = 5/6 * 2e = 5e/3
d/dx [-(1/6)(e)] = -1/6
d/dx [-(5/6)] = 0
Combining all the derivatives:
dy/de = e^2/2 + 5e/3 - 1/6
So, after evaluating the derivatives, the correct answer is:
dy/de = e^2/2 + 5e/3 - 1/6