If you're like me and don't remember hyperbolic identities (especially involving inverse functions) off the top of your head, recall the definitions of the hyperbolic cosine and sine:
Then differentiating yields
so that by the chain rule, if
then
Now, let , so that (•) .
Recall that
and so the derivative of tanh(<em>x</em>) is
where the last equality follows from the hyperbolic Pythagorean identity,
Differentiating both sides of (•) implicitly with respect to <em>x</em> gives
So, the derivative we want is the somewhat messy expression
and while this could be simplified into a rational expression of <em>x</em>, I would argue for leaving the solution in this form considering how <em>y</em> is given in this form from the start.
In case you are interested, we have
and you can instead work on differentiating that; you would end up with
Answer:
50
Step-by-step explanation:
Answer:
V≈94423.71
Step-by-step explanation:
V=πr2h=π·342·26≈94423.7088
Answer:
(1,4)
Step-by-step explanation:
2x-3y=-10
y=4x
Since the y is already isolated, you can use substitution to find the answer to this equation. Simply replace any y values in the first equation with 4x:
2x-3(4x)=-10
2x-12x=-10
-10x=-10
x=1
y=4(1)=4
Hope this helps!
Answer:
The Answer is B - (-1,2)
Step-by-step explanation:
A function must pass the vertical line test and if you were to plot any of those points on the graph they can't be on the same vertical line as any of the other points. (-1 , 2) is the only point that would allow the graph to pass the VLT