y=(3x^2 + x)/(squareroot of (x+6))
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use the rule for quotients
(denominator * derivative of numerator - numerator * denominator)/denominator^2
Btw squareroot of (x+6) is the same thing as (x+6)^(1/2), which I will be using.
(x+6)^(1/2) * (6x+1) - (3x^2 + x) (1/2)(x+6)^(-1/2)
______________________________________…
x + 6
^^^^ your answer
How I found the derivative of (x+6)^(1/2), which was (1/2)(x+6)^(-1/2)
take this section apart. You have an (x+6) and a ()^(1/2) on the outside.
Take the derivative of (x+6), which is 1, and multiply it by the derivative of ()^(1/2), which is
(1/2)()^(-1/2). Plug back in the (x+6) into the empty parenthesis.
(1/2)(x+6)^(-1/2)
(denominator * derivative of numerator - numerator * denominator)/denominator^2
Btw squareroot of (x+6) is the same thing as (x+6)^(1/2), which I will be using.
(x+6)^(1/2) * (6x+1) - (3x^2 + x) (1/2)(x+6)^(-1/2)
______________________________________…
x + 6
^^^^ your answer
How I found the derivative of (x+6)^(1/2), which was (1/2)(x+6)^(-1/2)
take this section apart. You have an (x+6) and a ()^(1/2) on the outside.
Take the derivative of (x+6), which is 1, and multiply it by the derivative of ()^(1/2), which is
(1/2)()^(-1/2). Plug back in the (x+6) into the empty parenthesis.
(1/2)(x+6)^(-1/2)
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I'm in 8th grade and I know this... so do your own homework.