find derivative of (3x^2 - 6x + 8)/(6x + 7)
rule: (u'v - uv')/(v^2)
(3x^2 - 6x + 8)/(6x + 7)
(6x - 6)(6x+7) - (3x^2 - 6x + 8)(6) / (6x+7)^2
(35x^2 + 6x - 42 - 18x^2 - 36x +48) / (6x+7)^2
(18x^2 - 30x + 6) / (6x+7)^2
what did I do wrong?
the answer is: (18x^2 + 42x – 90) / (6x + 7)^2
rule: (u'v - uv')/(v^2)
(3x^2 - 6x + 8)/(6x + 7)
(6x - 6)(6x+7) - (3x^2 - 6x + 8)(6) / (6x+7)^2
(35x^2 + 6x - 42 - 18x^2 - 36x +48) / (6x+7)^2
(18x^2 - 30x + 6) / (6x+7)^2
what did I do wrong?
the answer is: (18x^2 + 42x – 90) / (6x + 7)^2
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I'm not sure what JoelKatz is talking about, since you have correct formula in second line, and fourth line shows correct differentiation.
What you did wrong was expanding. So fifth line should be
(36x^2 + 6x - 42 - 18x^2 + 36x - 48) / (6x+7)^2
Notice 36x^2 instead of 35x^2 and also the signs on 36x and 48
Simplifying, we get:
(36x^2 - 18x^2 + 6x + 36x - 42 - 48) / (6x+7)^2
(18x^2 + 42x - 90) / (6x+7)^2
P.S. I'm thinking the error with 36x^2 was just a typo, since you actually got correct coefficient for x^2 in the end
What you did wrong was expanding. So fifth line should be
(36x^2 + 6x - 42 - 18x^2 + 36x - 48) / (6x+7)^2
Notice 36x^2 instead of 35x^2 and also the signs on 36x and 48
Simplifying, we get:
(36x^2 - 18x^2 + 6x + 36x - 42 - 48) / (6x+7)^2
(18x^2 + 42x - 90) / (6x+7)^2
P.S. I'm thinking the error with 36x^2 was just a typo, since you actually got correct coefficient for x^2 in the end
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(3x^(2)-6x+8)/(6x+7)
Find the derivative of the expression.
(d)/(dx) (3x^(2)-6x+8)/(6x+7)
Use the quotient rule to find the derivative of ((3x^(2)-6x+8))/((6x+7)). The quotient rule states that ((f)/(g))'=((f'g-fg'))/((g^(2))').
((d)/(dx) [(3x^(2)-6x+8)]((6x+7))-((3x^(2)-6x+8))(… [(6x+7)]))/(((6x+7))^(2))
Find the derivative of (3x^(2)-6x+8).
(d)/(dx) 3x^(2)-6x+8=6x-6
Find the derivative of (6x+7).
(d)/(dx) 6x+7=6
Substitute each function and derivative into the quotient rule formula.
(d)/(dx) (3x^(2)-6x+8)/(6x+7)=((6x-6)(6x+7)-(3x^(…
Simplify the derivative.
(d)/(dx) (3x^(2)-6x+8)/(6x+7)=(6x-6)/(6x+7)-(6(3x…
The derivative of ((3x^(2)-6x+8))/((6x+7)) is ((6x-6))/((6x+7))-(6(3x^(2)-6x+8))/((6x+…
(6x-6)/(6x+7)-(6(3x^(2)-6x+8))/((6x+7)…
Find the derivative of the expression.
(d)/(dx) (3x^(2)-6x+8)/(6x+7)
Use the quotient rule to find the derivative of ((3x^(2)-6x+8))/((6x+7)). The quotient rule states that ((f)/(g))'=((f'g-fg'))/((g^(2))').
((d)/(dx) [(3x^(2)-6x+8)]((6x+7))-((3x^(2)-6x+8))(… [(6x+7)]))/(((6x+7))^(2))
Find the derivative of (3x^(2)-6x+8).
(d)/(dx) 3x^(2)-6x+8=6x-6
Find the derivative of (6x+7).
(d)/(dx) 6x+7=6
Substitute each function and derivative into the quotient rule formula.
(d)/(dx) (3x^(2)-6x+8)/(6x+7)=((6x-6)(6x+7)-(3x^(…
Simplify the derivative.
(d)/(dx) (3x^(2)-6x+8)/(6x+7)=(6x-6)/(6x+7)-(6(3x…
The derivative of ((3x^(2)-6x+8))/((6x+7)) is ((6x-6))/((6x+7))-(6(3x^(2)-6x+8))/((6x+…
(6x-6)/(6x+7)-(6(3x^(2)-6x+8))/((6x+7)…
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You have not paid enough attention to the minus signs in moving from line 2 to line 3 of your working :
you have
(6x - 6)(6x+7) - (3x^2 - 6x + 8)(6) / (6x+7)^2
(35x^2 + 6x - 42 - 18x^2 - 36x +48) / (6x+7)^2
but the line just above should actually read
(35x^2 + 6x - 42 - 18x^2 + 36x - 48) / (6x+7)^2
. . . . . . . . . . . . . . . . . . . . . .↑ . . . ↑. . . . . . . . . . . . (these signs are the correct ones)
That's all.
you have
(6x - 6)(6x+7) - (3x^2 - 6x + 8)(6) / (6x+7)^2
(35x^2 + 6x - 42 - 18x^2 - 36x +48) / (6x+7)^2
but the line just above should actually read
(35x^2 + 6x - 42 - 18x^2 + 36x - 48) / (6x+7)^2
. . . . . . . . . . . . . . . . . . . . . .↑ . . . ↑. . . . . . . . . . . . (these signs are the correct ones)
That's all.
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wrong from (35x^2 + 6x - 42 - 18x^2 - 36x +48) !
Expand and simplify again (6x - 6)(6x+7) - (3x^2 - 6x + 8)(6)
Expand and simplify again (6x - 6)(6x+7) - (3x^2 - 6x + 8)(6)
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In the second line, you have (u'v-uv)/(v^2)
It should be (u'v-uv')/(v^2)
So the second (6x+7) should be 6.
It should be (u'v-uv')/(v^2)
So the second (6x+7) should be 6.