it would equal the same mixed number. 5 2/3
The picture is not clear. let me assume
y = (x^4)ln(x^3)
product rule :
d f(x)g(x) = f(x) dg(x) + g(x) df(x)
dy/dx = (x^4)d[ln(x^3)/dx] + d[(x^4)/dx] ln(x^3)
= (x^4)d[ln(x^3)/dx] + 4(x^3) ln(x^3)
look at d[ln(x^3)/dx]
d[ln(x^3)/dx]
= d[ln(x^3)/dx][d(x^3)/d(x^3)]
= d[ln(x^3)/d(x^3)][d(x^3)/dx]
= [1/(x^3)][3x^2] = 3/x
... chain rule (in detail)
end up with
dy/dx = (x^4)[3/x] + 4(x^3) ln(x^3)
= x^3[3 + 4ln(x^3)]
The correct answer would be 1in, if you want to check and see if im right use a 12 inch ruler and check
hope this helps out.
If Monday, then Chicken
If no Chicken, then no Monday
5 because you subtract 15x and bring it to 3x^2 and get 3x^2-15x=0. Then take out the gcf and you get 3x(x-5)=0. Since it can't be 0, x-5=0 , the answer is 5.
