Question

Please Help me with this one

calculate dy/dx

y = 7x^2 − 9x + 19 / 2x + 4

Answer 1

Is this the function?
\[\large y = \frac{7x^2 − 9x + 19}{ 2x + 4}\]

Answer 2

yes @CliffSedge

Answer 3

Familiar with the quotient rule?

Answer 4

"Low d-high minus high d-low all over low-squared"

Answer 5

or f'(x)g(x)-f(x)g'(x) / 2x+4

Answer 6

im just stuck on the next couple steps

Answer 7

For
\[\large y=\frac{f(x)}{g(x)}\]
\[\large y' = \frac{g(x)f'(x)-f(x)g'(x)}{(g(x))^2}\]

Answer 8

you have to square the (2x+4) on the bottom.

Answer 9

g(x) = 7x^2-9x+19 right?

Answer 10

I'm using g(x) for the denominator, so f(x)=7x^2-9x+19 and g(x)=2x+4

Answer 11

for f'(x) did you get f'(x)=14x-9. and for g'(x)= 2

Answer 12

Yes.

Answer 13

\[\frac{ 14x^2+56x-38 }{ (2x+4)^2 }\]

Answer 14

is that the correct answer?

Answer 15

Double check the constant in your numerator.

Answer 16

i got \[28x^2-18x+56x-36-14x^2+18x-38\]

- before solving

Answer 17

\[14x^2-20x+2\]

Answer 18

\(28x^2−18x+56x−36−14x^2+18x−38\)
\( = 28x^2−14x^2+18x−18x+56x−36−38 \)

Answer 19

Combine like terms to simplify.

Answer 20

got it . 14x^2+56x-74

Answer 21

Right, now also notice (if you want to simplify it), that you can factor \(\large 2^2\) out of the bottom and cancel a factor of 2 to reduce the fraction.

Answer 22

oh ok. thx for the help

Answer 23

My pleasure.