Recall that
d/dx sech(x) = - sech(x) tanh(x)
d/dx tan⁻¹(x) = 1/(1 + x²)
Then by the chain rule,
dy/dx = - sech(x) tanh(x) / (1 + x²)
Answer:
C.
Step-by-step explanation:
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Answer:
8 dollars per hour
Step-by-step explanation:
You make 92 a week
20 of that is from your allowance
92-20 = 72
72 is from your part time job
You work for 3 hours on Friday and 6 hours on Saturday, for a total of 3+6 = 9 hours
Take the amount of money earned and divide by the number of hours to determine the money earned per hour
72/9 = 8 dollars per hour

Divide both sides by
to get


Substitute
, so that
. Then



The remaining ODE is separable. Separating the variables gives

Integrate both sides. On the left, split up the integrand into partial fractions.




Then

On the right, we have

Solving for
explicitly is unlikely to succeed, so we leave the solution in implicit form,

and finally solve in terms of
by replacing
:


