Let and
. By the product rule,
By the power rule, we have and
, but
are functions of
, so we also need to apply the chain rule:
and we have
So we end up with
Replace to get everything in terms of
:
We can simplify this by factoring:
9514 1404 393
Answer:
3x -4y = -9
Step-by-step explanation:
Multiply by 4 to clear the fraction.
4(y -6) = 3(x -5)
Subtract the left-side term to get variables on the same side, with a positive x-coefficient.
0 = 3(x -5) -4(y -6)
Eliminate parentheses and collect terms.
0 = 3x -15 -4y +24
0 = 3x -4y +9
Subtract 9 and swap sides to get standard form.
3x -4y = -9
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Standard form is ...
ax +by = c
where a ≥ 0, and a, b, c are mutually prime integers. If a=0, then b > 0.
__
The attached graph shows the equations give the same line. The original line is shown dotted so that you can see they overlap.
